To solve the given equation, w need to review some rules:
The given equation is :
⇒⇒⇒⇒ rule (2)
⇒⇒⇒⇒ rule (1) and rule (2)
⇒⇒⇒⇒ rule (3)
removing the nature logarithm from both sides
∴ x = 4
So, the correct answer is option (2) ⇒⇒⇒⇒ x = 4
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The solution of the logarithmic equation is x = 4
What is Logarithm?The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm
The properties of Logarithm are :
log A + log B = log AB
log A − log B = log A/B
log Aⁿ = n log A
Given data ,
Let the logarithmic equation be represented as A
Now , the value of A is
[tex]ln[e^{ln ( x )} ] + ln[e^{ln (x^{2} )} ] = 2ln(8)[/tex]
On simplifying , we get
The value of ln e = 1
From the laws of logarithm , we get log Aⁿ = n log A
ln ( x ) ln ( e ) + ln ( x )² ln ( e ) = 2 ln ( 8 )
On further simplification , we get
ln ( x ) + ln ( x )² = ln ( 8 )²
From the laws of logarithm , we get log A + log B = log AB
ln ( x )³ = ln ( 64 )
ln ( x )³ = ln ( 4 )³
So , the value of x = 4
Hence , the logarithmic equation is solved
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if r(x) = 3x - 1 and s(x) = 2x , which expression is equivalent to (r/s) (6)
Step-by-step explanation:
(r/s)(x)=3x-1
2x
(r/s)(6)=18-1/12
=17/12
G(x)=(1/x+2) and h(x)=3x domain of g o h
Answer:
Step-by-step explanation:
( g o h)(x) = g(h(x)) = g(3x) = 1/(3x+2)
( g o h)(x) exisit for 3x+2 ≠ 0
x ≠ -2/3
so the domain is : D = ]-∞:-2/3[ U] -2/3;+∞[
How do you get 40y from the difference of 2 squares with the problem (5y+4+3x)(5y+4-3x)? I understand distribution method. I don't know where the 40y comes from using the special product method.
Answer:
Step-by-step explanation:
(5y+4+3x)(5y+4-3x) = (5y+4)² - (3x)²......(from the difference of 2 squares )
by identity : (a+b)(a-b) = a² - b²
in this exercice ; a = 5y+4 and b = 3x
An artist who was famous for his lifelike depictions of the human body during the Renaissance was
Answer:
Michelangelo Buonarroti was this artist.
Answer:
yes, the correct answer is D: Michelangelo
Step-by-step explanation:
I got it right in my quiz in edg 2020
hope this helps :)
If a number is a whole number then it is also a natural number
This statement is not true.
If a number is whole number, it will not always be a natural number. An example of a whole number that is not a natural number is 0. Think of natural numbers as counting number so 1, 2, 3, 4, ... and so on. Whole numbers are natural numbers but they also include 0. When we count up, we usually don’t starts with 0 so it’s not a natural number but it is a whole number.
Therefore, if a number is a whole number, it does not necessarily have to be a natural number.
Simplify 3 1/2 x 1/14
Answer:
0.25 or 1/4
Step-by-step explanation:
3 1/2 x 1/14 = 0.25
Answer:
-9 /14
= -0.6428571
Step-by-step explanation:
so basically, you simplify it by turning the mixed number into an improper fraction and then multiplying it (=-9/14) then, divide numerator by denominator and you have your answer! -0.6428571!!!
What is chlorination?
Answer:
Water chlorination is the process of adding chlorine or chlorine compounds such as sodium hypochlorite to water. This method is used to kill certain bacteria and other microbes in tap water as chlorine is highly toxic to those microorganisms. Answer via google.
Step-by-step explanation:
Answer: according to google
Step-by-step explanation:
Water chlorination is the process of adding chlorine or chlorine compounds such as sodium hypochlorite to water. This method is used to kill certain bacteria and other microbes in tap water as chlorine is highly toxic.
Type a definition for the following word.
fraction
Write an expression for the sequence of operations described below.
triple b, then multiply c by the result
Do not simplify any part of the expression.
The results of the expression; triple b, then multiply c by the result is b³ × c
ExpressionTriple b = b × b × b
= b³
triple b, then multiply c by the result= b³ × c
Therefore, the expression is written as b³ × c
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Final answer:
The expression for the sequence of operations described is (3 * b) * c.
Explanation:
To write an expression for the sequence of operations described, triple the variable b and then multiply the variable c by the result, you can use the following expression:
(3 * b) * c
In this expression, the variable b is tripled by multiplying it by 3, and then the variable c is multiplied by the result of tripling b.
What is the answer for this
If 7 ounces of cola costs $.59. How much should 19 ounces costs?
Answer:
$5.31
Step-by-step explanation:
If you times $.59 seven times you will get $4.13.
Then, you will have to add $.59 two times.
Finally, you will get $5.31 .
The cost will be $1.60 in the 19 ounces if the 7 ounces of cola costs $.59.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b, will be the denominator.
The proportion is a nature of a variable to another for example if we say x ∝ y then it will be a direct relation instant if we say x ∝ 1/y then it will be inverse relation.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given,
7 ounces ⇒ cost $0.59
Divide by 7 into both sides
7/7 ounces ⇒ cost $0.59/7
1 ounce ⇒ cost $0.084
Multiply both sides 19
19×1 ounce ⇒ cost $0.084 × 19
19 ounce ⇒ cost $1.60
Hence in 19 ounces of cola, it will cost $1.60.
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What is the domain of the function on the graph?
Dall real numbers
all real numbers greater than or equal to 0
all real numbers greater than or equal to -2
all real numbers greater than or equal to -3
Answer:
All real numbers greater than or equal to -3.
Step-by-step explanation:
The domain of a function is defined as the x values that are a part of the function. Therefore, looking at the graph, we see that the domain is all real numbers greater than or equal to -3, because the function doesn't contain x values less than -3.
What is ten times a number, increased by nine, is 59
Answer:
5
Step-by-step explanation:
10 times 5 = 50
50 + 9 = 59
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The number is = 5
Find the missing numberLet's take the number to be = X
Ten times a number= 10 × X = 10x
Increased by 9 is 59 = 10x + 9 = 59
To find X,
10x = 59 - 9
10x = 50
make X the subject of formula,
X = 50/10
X = 5
Therefore, the number is 5
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5. It is known that AABC = ADEF. If AB = 5, BC = 10, AC = 8, and DF = 2x-6, then solve for the value of
x. It would be helpful to draw two congruent triangles and carefully label the three vertices on each.
Answer:
The value of x is 7
Step-by-step explanation:
we know that
If two figures are congruent, then the corresponding angles and the corresponding sides are equal
In this problem
Triangles ABC and DEF are congruent
ABC≅DEF
therefore
AB=DE ----> equation A
AC=DF ----> equation B
BC=EF ----> equation C
Substitute the given values in the equation B
[tex]8=2x-6[/tex]
Solve for x
[tex]2x=8+6[/tex]
[tex]2x=14[/tex]
[tex]x=7[/tex]
therefore
The value of x is 7
The draw in the attached figure
In congruent triangles ABC and DEF, given side lengths in ABC and the length of side DF as 2x-6, we set this equal to the corresponding length in triangle ABC. Solving for x gives the result x=7.
Explanation:The subject of this question is Mathematics, specifically, the principle of congruent triangles in geometry. If two triangles are congruent, then their corresponding sides are equal. In the given congruent triangles, ΔABC and ΔDEF, AB corresponds to DE, BC to EF, and AC to DF. The length of DF is given as 2x-6, and its corresponding side AC in ΔABC is given as 8 units. Thus, we set 2x-6 equal to 8. Solving for x, we add 6 to both sides of the equation, resulting in 2x = 8 + 6. This simplifies to 2x = 14. Finally, dividing both sides by 2 results in x = 7.
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calculate: 3 gallons = ? liters
Answer:
There is exactly 11.3562 liters of liquid but to round it would be about 11.36 liters of liquid
Step-by-step explanation:
1 gallon =3.78541 liters
What is a part of a line hat consists of two points called endpoints, and all the points on the line that are between the endpoints
Answer:
i think that is called a line segment
Step-by-step explanation:
Answer:
line segment
Step-by-step explanation:
What is 5.5 divided by 3.5
5.5 divided by 3.5 is 1.57142857 when solved, but when rounded, you will get 1.6, or 1.57.
Hope this helped!
Nate
RJ read 40 pages of gis book in 50 minutes. How many pages can I read in 80 minutes?
Answer:
64 pages
Step-by-step explanation:
40 pg = 50 min
8 pg = 10 min
64 pg = 80 min
a solid wooden cone with diameter 14cm and vertical length 24cm is vertically cut into two equal halves. one half is to be covered by paper at rate of rs 7per sq. cm find total cost of paper required?
Answer:
V = 392[tex]\pi[/tex]
Step-by-step explanation:
The volume of a cone is: V = [tex]\frac{1}{3} \pi r^{2} h[/tex]
diameter = 14 h = 24
diameter = 2r ---> r = 7
V = [tex]\frac{1}{3} \pi (7)^{2} (24)[/tex]
V = [tex]\frac{1}{3} \pi (49)(24)[/tex]
V = [tex]\frac{1}{3} \pi (1176)[/tex]
V = 392[tex]\pi[/tex]
Find each product.
1. 1(-2)
Think: 1 x 2 = 2. A negative and a
positive integer have a negative product.
In order to get the answer to this question you will have to multiply a positive times a negative and it will equal a negative.
[tex]1(-2)[/tex]
[tex]1\times(-2)=[/tex]
[tex]1\times(-2)=-2[/tex]
[tex]=-2[/tex]
Therefore your answer is "-2."
Hope this helps.
Chris has 2 pairs of black socks, 4 pairs of red socks, and 18 pairs of white socks in a dresser drawer. What is the probability that he will choose a pair of white socks, without looking in the drawer first?
75%
0.33
50%
Answer:
75%
Step-by-step explanat
Find the total pairs:
2 +4 +18 = 24 total pairs.
18 pairs are white.
The probability is the number of white over the total number of pairs:
18/24 = 0.75 = 75%
The answer is 75%
What is 2 19 over 20 terminating or repeating
Answer:
terminating
Step-by-step explanation:
20 is a factor of a 100
20 × 5 = 100
therefore 19 × 5= 95
So in decimal form it's 2.95
4x-9= 3.5-9 please help!
Answer:
x = 7/8
Step-by-step explanation:
7/8 of 4 is 3.5
4x-9 = 3.5-9
In circle O, what is m? 50° 55° 125° 250°
Answer:
The measure of angle JAM is 55°
Step-by-step explanation:
The correct question is
Find the measure of angle JAM
See the attached figure to better understand the problem
step 1
Find the measure of angle JAK
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
so
m∠JAK=(1/2)[arc KJ+arc LM]
substitute the given values
m∠JAK=(1/2)[170°+80°]=125°
step 2
Find the measure of angle JAM
we know that
m∠JAK+m∠JAM=180° ------> by supplementary angles
we have
m∠JAK=125°
substitute
125°+m∠JAM=180°
m∠JAM=180°-125°=55°
Answer:
The answer is 55
Step-by-step explanation:
A living room measures 24 feet by 15 feet. An adjacent square dining room measures 13 feet on each side. If carpet costs $6.98 per square foot, what is the total cost of putting carpet in both rooms?
Answer:
total cost of putting carpet in both rooms is $3692.42
Step-by-step explanation:
given data
living room length = 24 feet
living room width = 15 feet
dining room is square so length and width will be same
dining room length = 13 feet
dining room width = 13 feet
carpet costs = $6.98 per square foot
to find out
what is the total cost of putting carpet in both rooms
solution
first we find the total area of both room that is
area of living room = length × width .................1
area of living room = 24 × 15
area of living room = 360 feet² ...........................2
and
areas of dining room = length × width
area of dining room = 13 × 13
area of dining room = 169 feet² ...............................3
so total area = add equation 1 and 2
total area = 360 feet² + 169 feet²
total area = 529 feet²
and
total cost of putting carpet in both rooms are = total area × carpet costs .................4
put here value
total cost of putting carpet in both rooms = 529 × $6.98
total cost of putting carpet in both rooms =$3692.42
The calculated total square footage that needs carpeting is 529 square feet. At $6.98 per square foot, the total cost of carpeting both rooms would be $3,690.42.
Explanation:The subject of this problem is mathematics, specifically the topic of area calculations and cost analysis. First, calculate the area for both rooms. The area of a rectangle is given by the formula length x width, so the area of the living room is 24 feet x 15 feet which equals 360 square feet. As the dining room is a square, its area is side x side, thus 13 feet x 13 feet equals 169 square feet.
Then, add these to get the total square footage that will need carpeting, which is 360 + 169 = 529 square feet.
Lastly, multiply this total area by the cost per square foot for carpeting. This gives $6.98 x 529 square feet = $3,690.42. So, the total cost of carpeting both rooms would be $3,690.42.
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Choose the correct expression to represent the situation: The cost of a telephone call is $1.25 plus 50 cents times the number of minutes (m). *
1.25 + 0.50m
1.25m + 0.50
1.25 + 0.50 + m
Answer:
1.25 + 0.50m
Step-by-step explanation:
This is because 1.25 is the call fee plus 50 cents per minute, the word per is a key word for multiplication there for 50 times m so the equation is $1.25 fee + 0.50m
To convert a distance of 12,000 feet to miles, which ratio could you multiply
by?
5280 feet
1 mile
1 mile
5280 feet
O c. 52podle
1 foot
5280 miles
D
12 inches
1 foot
Answer:
1 mile = 5280 feet
Step-by-step explanation:
To convert a distance of 12,000 feet to miles, we use this ratio:
1 mile = 5280 feet
? = 12,000 feet
Cross multiplying gives;
[tex]\frac{12,000}{5,280}[/tex] × 1 mile = 2.272727273 miles.
Answer:
B.
Step-by-step explanation:
Jackson is a 25 year old college student whose parents contribute to his support. His parents may claim him as a tax dependent in 2011 as long as They don't turn his bedroom into a home office. he makes under $500. he is under 30. they contribute more than half of his support for the year.
Answer:
Bot
Step-by-step explanation:
Julia asked to evaluate the expression four to the power of -3 before she can join her classmates outside. She decides to use the value of the expression to help choose which activity to do. If the value is greater on she’ll play basketball. Value is equal to one, she play soccer. If the value is less than 1to play tennis. Which activity is Julia going to do today?
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The value is less than 1.
She will play tennis today.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
[tex]4^{-3}[/tex]
We will evaluate this expression.
[tex]4^{-3}[/tex] can be written as [tex]\frac{1}{4^{3} }[/tex]
This means,
= 1/(4 x 4 x 4)
= 1/64
= 0.016
This is less than 1.
We have,
If the value is greater than 1, she’ll play basketball.
If the value is equal to 1, she plays soccer.
If the value is less than 1, she will play tennis.
The value is less than 1.
Thus,
The value is less than 1.
She will play tennis.
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The expression 'four to the power of -3' equals 0.015625. Since this value is less than 1, Julia will play tennis.
Explanation:To evaluate the expression four to the power of -3, we have to understand how negative exponents work. A negative exponent means to divide 1 by the base raised to the power of the absolute value of the exponent. So 4^-3 is equivalent to 1/(4^3).
Let's do the maths:
4^3 = 4 * 4 * 4 = 64.
Then, 1/64 = 0.015625.
Therefore, four to the power of negative three is 0.015625.
Julia will choose activities based on the value of the expression - since the value is less than 1, in this case, she would play tennis.
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What is the remainder when 16,055 is divided by 16? (Input numeric values only)
Answer:
16055=16000+55
16000mod16=0
55mod16=7
(7+0)mod16=7
its 7