Express the given quantity as a single logarithm. ln x + a ln y − b ln z

Answers

Answer 1

The rules of logarithms tell you ...
• [tex]\ln(a)+\ln(b)=\ln(a \cdot b)[/tex]
• [tex]a \cdot \ln(b)=\ln(b^{a})[/tex]

[tex]\ln(x)+a \cdot \ln(y)-b \cdot \ln(z)=\ln\left( \dfrac{x \cdot y^{a}}{z^{b}} \right)[/tex]

Answer 2

Final answer:

To express ln x + a ln y - b ln z as a single logarithm, use the properties of logarithms.

Explanation:

To express ln x + a ln y - b ln z as a single logarithm, we will use the properties of logarithms. The key properties we will use are:

ln xy = ln x + ln y: The logarithm of a product is the sum of the logarithms of the factors.ln (x/y) = ln x - ln y: The logarithm of a quotient is the difference of the logarithms of the numerator and denominator.

Using these properties, we can simplify the expression:

ln x + a ln y - b ln z = ln x + ln(y^a) - ln(z^b)= ln (x(y^a)/(z^b))

So, the given quantity can be expressed as a single logarithm: ln (x(y^a)/(z^b))

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Related Questions

PLEASE HELP ASAP Arrange the expressions in increasing order of their values.

(10⁰x 10¹ x 1¹⁰) (10 x 10¹) (10⁰+10¹+1¹⁰) (10⁰+10¹x 1¹⁰)

Answers

For this case we have the following expressions:
(10⁰x 10¹ x 1¹⁰)
(10 x 10¹)
(10⁰ + 10¹ + 1¹⁰)
(10⁰ + 10¹x 1¹⁰)
Rewrite we have:
(1x 10 x 1) = 10
(10 x 10) = 100
(1 + 10 + 1) = 12
(1 + 10x 1) = 11
Answer:
In increasing order we have:
(10⁰x 10¹ x 1¹⁰)
(10⁰ + 10¹x 1¹⁰)
(10⁰ + 10¹ + 1¹⁰)
(10 x 10¹)

Final answer:

After calculating the values of the expressions, they can be arranged in increasing order of their values as follows:

(10⁰x 10¹ x 1¹⁰), (10⁰ + 10¹x 1¹⁰), (10⁰ + 10¹ + 1¹⁰), (10 x 10¹).

Explanation:

To arrange the expressions in increasing order of their values, we must first calculate the value of each expression.

(10⁰ x 10¹ x 1¹⁰): Here, 10⁰ = 1, 10¹ = 10, and 1¹⁰ = 1 (since any number to the power of zero is 1). Multiplying these together, we get 1 x 10 x 1 = 10.(10 x 10¹): This equals 10 x 10 = 100.(10⁰+10¹+1¹⁰): Adding these values together gives us 1 + 10 + 1 = 12.(10⁰+10¹ x 1¹⁰): Following the rules of operations (multiply before adding), first calculate 10¹ x 1¹⁰ which equals 10 x 1 = 10, then add 10⁰ which is 1. So, this gives 1 + 10 = 11.

Now we can arrange the expressions in increasing order:

(10⁰x 10¹ x 1¹⁰) (10⁰ + 10¹x 1¹⁰) (10⁰ + 10¹ + 1¹⁰) (10 x 10¹)

Find a negative real number such that the square of the sum of the number and
25 is equal to 36

Answers

"The square of the sum of the number and 25 is equal to 36" translates to
[tex](n+25)^2=36[/tex]

Take square root of both sides:

[tex]|n+25|=6\quad\Longrightarrow\quad n+25 = 6\ \text{ or }\ n+25=-6[/tex]

Then subtract both sides by 25:

[tex]n = 6-25\ \text{ or }\ n=-6-25\\\ \\\boxed{n=-19\ \text{or}\ n=-31}[/tex]

Hope this helps.

Identify one characteristic of exponential growth.

A. A graph that is an increasing curve
B. A common ratio between 0 and 1
C. A common ratio less than 0
D. A common difference greater than 0

Answers

A. Exponential growth is called growth because it increases, so A is correct.
B. A common ratio between 0 and 1 would result in decay, not growth
C. A common ratio less than one would just reflect the graph across the x-axis. It does not give any information about whether or not it is exponential growth.
D. Exponential growth functions have no common differences.

Thus, A is the correct answer.

Exponential growth features a quantity increasing at a constant growth rate. The correct answer is Option A.

Exponential growth is characterized by a situation where a quantity increases at a constant growth rate. It is often represented graphically by an increasing curve.

This means that as time progresses, the rate at which the quantity grows also increases. For example, the population of a species might grow slowly at first, but as it becomes larger, the growth rate accelerates.

Given the options in the question, the correct answer is:

Option A. A graph that is an increasing curve

Sam entered three functions into a graphing calculator, y1 = x + 2, y2 = x2 + 2, and y3 = 2x. A portion of the table created by those functions is shown below.

Answers

We have the following functions:
y1 = x + 2
y2 = x ^ 2 + 2
y3 = 2 ^ x

For x = 0:
y1 = 0 + 2 = 2
y2 = 0 ^ 2 + 2 = 0 + 2 = 2
y1 = y2

For x = 5
y2 = 5 ^ 2 + 2 = 25 + 2 = 27
y3 = 2 ^ 5 = 32
y3> y2

For x = -1:
y1 = -1 + 2 = 1
y2 = (-1) ^ 2 + 2 = 1 + 2 = 3
y3 = 2 ^ (- 1) = 1/2 = 0.5
y3 <y1 <y2

Answer:
y1 = y2
y3> y2
y3 <y1 <y2

WANT TO BE THE BRAINLIEST PLZ ANSWER STEP BY STEP

Answers

A and C, because the others are incorrect, if you look at the chart you can see that B and D are not true as its the complete opposite.

The answer is c because hip hop is preferred more than country in the 9-11 age group

the hall family garden is 3/4 of an acre. if they divide their garden into 1/8 acre sections, how many sections will they have?

Answers

we know that
The hall family garden is ------------> 3/4 of an acre
if they divide their garden into 1/8 acre sections
so
(3/4)/(1/8)-------> (3/4)*(8)--------> 8*3/4------> 24/4-----> 6 sections

the answer is
6 sections

Answer:

6 sections

Step-by-step explanation:

A lifeboat can carry up to 24 people. Write an inequality to represent this situation

Answers

the inequality is n<24
hoped it helped
brainlist plz

If x represents the number of people that the lifeboat is carrying, and the lifeboat can be empty at the very least, then the inequality would be: 0[tex] \leq [/tex]x[tex] \leq [/tex]24

at elm elementary school for every 5 students who walk to school there are 7 students who take the bus.if 420 students attend elm elementary school how many of them walk to school? tell me how you got the answer and will mark brainliest

Answers

175 students walk to school. 7+5=12 and 420 divided by 12 is 35. I checked how I did it was correct because of 5*35+7*35=420. Then I found the product of 5*35 which is 175.

The students walk to school is 175.

What is Ratio?

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

let the ratio of students who walk to students who take bus = 5: 7

let the common ratio be x.

So, Number of students who walk = 5x

and, Number of students who Bus= 7x

Total students= 420

So, 5x+ 7x = 420

12x= 420

x= 35

Hence, students walk to school =5 x 35 = 175.

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2.
Find the annual percentage rate, using the annual percentage rate table.
Amount Financed: $8,900

Finance Charge: $1,030.62

Number of Payments: 24

Answers

Amount Financed: $8,900
Finance Charge: $1,030.62
Number of Payments: 24

(Finance Charge)/(Amount Financed)*100$=($1,030.62)/($8,900)*100$
(Finance Charge)/(Amount Financed)*100$=(0.1158)*100$
(Finance Charge)/(Amount Financed)*100$=$11.58

In the row of number of Payments 24, we look for:
(Finance Charge)/(Amount Financed)*100$=$11.58, and we to which annual porcentage rate it corresponds in the first row

Answer: The annual percentage rate is 10.75%

Factor completely a2 - 9a + 20

Answers

(a - 5)(a - 4)
You can check, the numbers add up, because -5 - 4 is 9, and 5 * 4 is 20

a^2-9a+20=a^2-5a-4a+20=(a^2-5a)+(-4a+20)
a^2-9a+20=a(a^2/a-5a/a)+(-4)(-4a/(-4)+20/(-4))
a^2-9a+20=a(a-5)-4(a-5)
a^2-9a+20=(a-5)[a(a-5)/(a-5)-4(a-5)/(a-5)]
a^2-9a+20=(a-5)(a-4)

During a basketball game a player makes 12 of 18 free throws attempted write the ratio as fraction reduced to the lowest term

Answers

To make this a fraction, let's put [tex] \frac{12}{18} [/tex] . We can divide both top and bottom by 6, leaving us with [tex] \frac{2}{3} [/tex] . This is as far as we can reduce it, making it your answer. I hope this helps!

Final answer:

The ratio of free throws made to free throws attempted by the player is 12/18, which can be reduced to its lowest terms by dividing both numbers by their greatest common divisor, 6, resulting in the reduced fraction 2/3.

Explanation:

To find the ratio of free throws made to free throws attempted, we start by looking at the numbers given: 12 made out of 18 attempted. We express this ratio as a fraction 12/18.

To reduce this fraction to its lowest terms, we need to find the greatest common divisor (GCD) that divides both numerator and denominator evenly.

In this case, the number 6 is the GCD of 12 and 18. Dividing both the numerator and the denominator by 6, we get 2/3.

Hence, the ratio of free throws made to free throws attempted, reduced to the lowest term, is 2/3.

A collection of dimes and quarters worth $9.25. There are 46 coins in all. Find how many of each there are. How many dimes are there?

Answers

If all were quarters, the value would be 46*$0.25 = $11.50. The actual value is $2.25 less than that. Replacing a quarter with a dime reduces the value by $0.15, so there must be $2.25/$0.15 = 15 dimes

There are 15 dimes.

Find the greatest common factor of 30 and 60

Answers

The greatest common factor of 30 and 60 is 15 because 15 times 2 is 30 and 15 times 4 is 60.

I hope this helped

Hey can you please help me posted picture of question

Answers

Answer: option C. Emily got 12 text messages, adn 5 were from Jasmine. The probability a text message is from Jasmine is 5/12.

Explanation:

All the other options are theoretical probabilities because they were determined using the equation:

probablity = number of positive events / total number of possible events.

While, experimental probabilities are determined from actual results of an experiment (test). That is what the option C. describes. It compares the number of times that she actually got a message (5) with the number of trials (12). It is not determined theoretically.

BRAINLIEST!!!!

Triangle Z' is the image of triangle Z after a series of transformations.
Aliyah and Ivan described the sequence of transformations in different ways.
Which sequence or sequences are correct and why?

GRID AND ANSWERS PROVIDED IN IMAGES!

Answers

Both Aliyah and Ivan are correct because both chose the correct scale factor for the dilation and both describe other transformations that would produce triangle .

Answer:

The third option is correct.

Step-by-step explanation:

Calculate the average rate of change of f(x) over the interval [-4, -1] using the formula [ BLANK ] The value of f(-1) is [BLANK] The value of f(-4) is .[BLANK] The average rate of change of f(x) over the interval [-4, -1] is .[BLANK]

First set of answers: A. [f(-4)-f(-1)]/[-5]
B.[f(-1)-f(-4)]/[-5]
C.[f(-1)-f(-4)]/[3]
D.[f(-4)-f(-1)]/[3]

Second set of answers: A.3 Third set: A.-4 Final set A.-2
B.2 B.-3 B.-1.5
C.-1 C.4 C.2
D.4

Answers

Answers:
The formula is [f(-1)-f(-4)]/[3]
The value of f(-1) is 3
The value of f(-4) is -3
The average rate of change is 2

==============================================

Explanation:

For the first blank, we use the formula
[ f(b) - f(a) ]/[ b - a ]
where 'a' and 'b' are the endpoints for the x interval

In this case, a = -4 and b = -1. When you plug those values into the formula above, you get...
[ f(b) - f(a) ]/[ b - a]
[ f(-1) - f(-4)]/[ -1 - (-4) ]
[ f(-1) - f(-4)]/[ -1+4 ]
[ f(-1) - f(-4)]/[ 3 ]
which is why the answer is choice C for the first blank

-------------------------------------------

To compute the value of f(-1), we draw a vertical line through -1 on the x axis. This vertical line crosses the diagonal function graph at the point (-1,3). The y value of this point is what we want. Plugging in x = -1 leads to y = 3. This is why f(-1) = 3
If you want, you can draw a horizontal line through (-1,3) and you'll see it touching 3 on the y axis.

-------------------------------------------

Follow similar steps as above to compute f(-4). Draw a vertical line through x = -4 on the x axis. Mark the point where the vertical line crosses the diagonal line. This point is (-4,-3). Optionally draw a horizontal line over til you hit the y axis and you'll find that y = -3 corresponds to x = -4

This is why f(-4) = -3

-------------------------------------------

We'll use the last three sections to compute the average rate of change. Everything combines together building up to this moment.

From the first part, we had the formula
[ f(b) - f(a) ]/[ b - a ]
[ f(-1) - f(-4)]/[ 3 ]

We can replace the "f(-1)" with 3 since we found that f(-1) = 3
Similarly, f(-4) = -3 so we can replace the "f(-4)" with -3

Doing those replacements and simplifying leads to...

[ f(-1) - f(-4)]/[ 3 ]
[ 3 - (-3)]/[ 3 ]
[ 3 + 3]/[ 3 ]
6/3
2

So the average rate of change is 2

Note: because the entire graph is a straight line, the average rate of change for any interval a < x < b is going to be equal to the slope m. In this case, the slope of the line is m = 2/1 = 2. We move up 2 units each time we move to the right 1 unit along the diagonal line.

NEED HELP ASAP PLEASE

Answers

Divide any term by the previous term.

For example,

(3/28) / (-1/4) = 3/28 * (-4/1) = -12/28 = -3/7

Answer: -3/7

# 14. Q. find the area of rectangle

Answers

The answer is 112 ft^2

You must multiply the height and the width.

8 x 14 = 112

Area of a rectangle is the product of its Length and Width.

Area = Length x Width

From figure we can see,

Length = 14 ft
Width = 8 ft

So, Area = 14 x 8 = 112 ft²

Thus, the option third gives the correct measure of Area for given rectangle

A rectangular table is six times as long as it is wide. If the area is 294 ftsquared, find the length and the width of the table.

Answers

42 length 7 width
please respond back if it was correct

the width of a rectangular table is 7 feet and the length of a rectangular table is 42 feet.

The area of a rectangular table is 294 ft².

What is the area of a rectangle?

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Let the width of a rectangular table be x.

Then, six times as long as it is wide = 6x

Area of a rectangular table = 6x × x

⇒ 6x²=294

⇒ x²=49

⇒ x=7 feet

So, length=6x=42 feet

Therefore, the width of a rectangular table is 7 feet and the length of a rectangular table is 42 feet.

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Analyze the diagram below and complete the instructions that follow.

Solve for y.

Answers

Y= 10 because you have a 180 degree angle split in half which equals 90 degrees so 3•30=90 the the other side has to equal 90 degrees so 2•30=60 then 3•10=30 so then just add 60 and 20 and there is your 90

Two trucks started traveling from the same place at 9:00 a.m. One truck traveled North going 45 mph and the other traveled South going 50 mph. What time will it be when the trucks are 380 miles apart?

Answers

Short Answer 1 PM
Givens
South bound truck's rate = 50 mph
North bound truck's rate = 45 mph
Distance apart = 380 after time t
The time that passes = t

Equations
d = r * t
d1 + d2 = 380
d1 = r_south * t
d2 = r_north * t

Substitute and solve.
r_south * t + r_north * t = 380
50*t + 45*t = 380 Combine like terms.
95t = 380 Divide by 95
t = 380 / 95
t = 4 hours

Answer
t = 9:00 + 4 hours = 1300 hours = 1:00 PM <<<< answer

Answer: 1:00 PM

Step-by-step explanation:

Hey can you please help me posted picture of question

Answers

The statement above is TRUE.
When two probabilities are multiplied together, then the probability represents a compound event. In probability, a compound event refers to two or more events that are happening simultaneously. The calculation goal is usually to find the probability of all those events actually occurring.

Hey can you please help me posted picture of question

Answers

Sample Space is the set of all possible outcomes that could occur for an event.

For example, sample space for tossing a coin will be {H, T} ,where H stands for Head and T stands for Tail

Likewise sample space for throwing a dice will be: {1, 2, 3 ,4, 5 ,6}

Thus, the answer to this question is option A

The appropriate definition is ...
A. The set of all possible outcomes.

Find the area in the first quadrant under the curve y = 1 / (x^2+6x+10)

Answers

The area is given by

[tex]\displaystyle\int_0^\infty\frac{\mathrm dx}{x^2+6x+10}[/tex]

Complete the square in the denominator:

[tex]x^2+6x+10=x^2+6x+9+1=(x+3)^2+1[/tex]

then substitute [tex]x+3=\tan y[/tex], so that [tex]\mathrm dx=\sec^2y\,\mathrm dy[/tex]. Then as [tex]x\to0^+[/tex], we have [tex]y\to\arctan3[/tex]; as [tex]x\to\infty[/tex], we have [tex]y\to\dfrac\pi2[/tex]. So the integral becomes

[tex]\displaystyle\int_{\arctan3}^{\pi/2}\frac{\sec^2y}{\tan^2y+1}\,\mathrm dy=\int_{\arctan3}^{\pi/2}\mathrm dy=\dfrac\pi2-\arctan3[/tex]

Find the area for the given shape below

Answers

To find the area of a triangle given its base and its height, use the formula A = bh/2.

The base of the triangle is 14m.
The height of the triangle is 10m.

Plug these values into the formula and solve.

A = bh/2
A = 14(10)/2
A = 140/2
A = 70

Answer:
The area of the triangle is 70 m².

15 + (-18) =
Please help quick

Answers

-3

hope this help........................

12% of 250 is what answer

Answers

The answer is 30.

Hope this helped :)
alisa202

Mary used a thermometer to measure the temperature of water at different states. What would the Celsius thermometer read when water froze and became a solid ?
A) -32 o
B) 0 o
C) 25 o
D) 32 o

Answers

it would be answer choice B) 0^o (0 degrees)

It would be B in Celsius

"A magician performing a magic act has asked for 2 volunteers from the audience to help with his routine. If there are 250 people in the audience, which of the following expressions represents the number of possible pairs of volunteers?"

Answers

The answer should be 250 objects taken 2 at a time

Number of people in the audience = 250

Number of volunteers required to perform the magic act from the audience =2

As 2 people can be selected from 250 people by using the properties of combination as order of choosing people is not important.

Possible number of ways = [tex]_{2}^{250}\textrm{C}[/tex]

= [tex]\frac{250!}{2!\times 248!}=249 \times 125=[/tex]

= 31125 ways

GETS BRAINLIEST AND 11 PTS!

Maggie has 7 tiles with pictures of plants and 2 tiles with pictures of animals. Maggie keeps all the tiles on a mat with the pictures hidden and mixes them up. She then turns one tile face up and finds the picture of a plant on it. She removes this tile from the mat and turns over another tile without looking. What is the probability that the second tile that Maggie turns over has a plant on it? 22.2% 28.6% 65.0% 75.0%

@musiclover10045

Answers

I believe the answer to this one would be 75.0%

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In the 1800s, the work of raising tobacco, rice, or cotton on plantations in the South was done by _____. 1. enslaved people from Africa and the West Indies 2. English, Scottish, and Irish immigrants 3.Mexican and Cuban immigrants 4. enslaved people from the Natchez, Creek, and Cherokee tribes Perform the operation 8 1/2 + 5 1/8 May someone help me? Please the prosecutor repeated herself and spoke very loudly and clearly to the jury to help ________ her point a. illustrate b. illuminate c. demonstrate d. emphasize For the triangle above, find sin A. a. 36 c. 0.9323 b. 50 d. 0.385 Imagine that you were in the same situation as Harrison Bergeron would you have acted the way he did or would you have done something different? Why? which organ is involved in ingestion At which stage of nrem sleep will you feel most groggy if you are suddenly awakened from it? What is the standard deviation of the data set? 29, 36, 41, 53, 45, 30, 60 {d}ulcea.English dc.extremely soft/omittedb.English th An average infant is 20 inches long and weighs 7.6 pounds. if the child grows to 80 inches and keeps the same proportions,how much will the child weigh A temporary suspension of the menstrual cycle normally occurs during Read the excerpt below and answer the question. "This will be worse than the windmills, said Sancho. Look, senor; those are friars of St. Benedict, and the coach plainly belongs to some travellers: I tell you to mind well what you are about and dont let the devil mislead you. I have told thee already, Sancho, replied Don Quixote, that on the subject of adventures thou knowest little. What I say is the truth, as thou shalt see presently." Which theme from Don Quixote is present in this excerpt? reality vs. fantasy tradition vs. change knowledge and books chivalry and courtly love Of all planets in our system jupiter has the greatest gravitational strength The concern with getting daughters married into good families pervades Jane Austen's Pride and Prejudice and forms a large part of the social mannerisms that the novel mocks. In which lines in this excerpt does one of the Bennet parents make an ironically false claim about having gone to great lengths to achieve that goal? What is the first quartile of the data set? {51, 42, 46, 53, 66, 70, 90, 70} A-48.5 B-59.5 C-61 D-80 solve for x 19-24. find the measure of the angle indicated in bold for 25-28. Is an intentional burn that removes fuel and oxygen from an advancing fire? #28: Describe/explain three different types of waves regularly used by humans. An oxidation reaction occurs only in the presence of _____.