Solve 2 log 2x = 4. Round to the nearest thousandth if necessary

Answers

Answer 1

Answer:
x = 50

Explanation:
Before we begin, remember the following:
logₐ (x) = b
is equivalent to:
aᵇ = x

log with no base written has the default base 10

Now, let's check the given:
2 log 2x = 4

We will start by dividing both sides by 2:
log 2x = 2

Now, applying the above rules, we can get the value of the x as follows:
log 2x = 2
10² = 2x

[tex] \frac{2x}{2} [/tex] = [tex] \frac{10^2}{2} [/tex]

x = 50

Hope this helps :)

Answer 2

Answer:

For [tex]2log2x=4[/tex] , x = 50

Step-by-step explanation:

Given : [tex]2log2x=4[/tex]

We have to find the value of x.

Consider the given [tex]2log2x=4[/tex]

Divide both side by 2, we have,

[tex]\frac{2\log _{10}\left(2x\right)}{2}=\frac{4}{2}[/tex]

Simplify, we have,

[tex]\log _{10}\left(2x\right)=2[/tex]

[tex]\mathrm{Apply\:log\:rule}:\quad \:a=\log _b\left(b^a\right)[/tex]

[tex]2=\log _{10}\left(10^2\right)=\log _{10}\left(100\right)[/tex]

[tex]\log _{10}\left(2x\right)=\log _{10}\left(100\right)[/tex]

When log have same base, we have,

[tex]\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\quad \Rightarrow \quad f\left(x\right)=g\left(x\right)[/tex]

We have,

[tex]2x=100[/tex]

Divide both side by 2, we have,

[tex]x=50[/tex]

Thus, For [tex]2log2x=4[/tex] , x = 50

Related Questions

Solve the equation 2cos^2x = sin2x , giving your answer in terms of π. 0

Answers

2cos^2x = sin2x 2cos^2x = 2sin x cos x (2sin x cos x) / (2cos^2x) = 1 sin x / cos x = 1 tan x = 1 x = π/4

Given is [tex] 2*cos^{2} (x)=sin(2x) [/tex]

We can use following formulas to solve this problem :-

1. [tex] \frac{sin\;\theta}{cos\;\theta} = tan\;\theta [/tex]

2. sin(2∅) = 2·sin(∅)·cos(∅)

Solving the given equation :-

[tex] 2*cos^{2} (x)=sin(2x) \\\\2*cos^{2} (x)=2*sin(x)*cos(x) \\\\2*cos^{2} (x)-2*sin(x)*cos(x)=0 \\\\2*cos^{2}(x)*(1-\frac{sin(x)}{cos(x)}) =0 \\\\2*cos^{2}(x)*(1-tan(x)) =0 \\\\cos^{2}(x) = 0 \;or\; (1-tan(x)) =0 \\\\cos(x) = 0 \;or\; tan(x) =1 \\\\x = cos^{-1}(0) \;or\; x=tan^{-1}(1) \\\\x=\frac{\pi}{2} \;or\; x=\frac{\pi}{4} [/tex]

Hence, final answer is [tex] x=\frac{\pi}{2} \;or\; x=\frac{\pi}{4} [/tex].

The length of a rectangular garden is 7 feet longer than its width. if the garden's perimeter is 182 feet, what is the area of the garden in square feet?

Answers

182 - 14=168
168/2
=84
84+7=91
91x84 = 7644 square feet

7644 square feet :))))))))

Point A is located at (0, 4) and point B is located at (−2, −3). Find the x value for the point that is 1/4 the distance from point A to point B.

−1

−0.75

−0.5

−0.25,

Answers

- First thing, find the distance between A and B:

AB =[tex] \sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} } [/tex] =
=[tex] \sqrt{(0-(-2))^{2} + (4-(-3))^{2} } [/tex] =
= [tex] \sqrt{4+49} [/tex] =
= √53

- Hence, we know that the distance between point A and the point C to be found is:
AC = √53 / 4

- The only other thing we know about point C is that it lays on the line that connects A and B. Let's use the point-slope formula to find the equation of this line:

y - y₂ = [tex] \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex] (x - x₂)
y - (-3) = (7/2)(x - (-2))
y + 3 = (7/2)(x + 2)
y = (7/2)x + 7 - 3
y = (7/2)x + 4

This is the equation that ties the coordinates of every point laying on it, therefore it is vaid for A, B and, above all, C which will be:
C (x , (7/2)x + 4)

- Now let's find the distnce between A and C:
AC =[tex] \sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} } [/tex]=
=[tex] \sqrt{(x-0)^{2} + ((7/2)x+4-4)^{2} } [/tex] =
=[tex]\sqrt{x^{2} + (49/4)x^{2} }[/tex] =
=[tex] \sqrt{(53/4) x^{2} } [/tex] =
=+/-(√53/2)x
- Lastly, we know this distance must be equal to √53 / 4, therefore you need to set and solve the equation:
+/-(√53/2)x = √53 / 4
(1/2)x = +/-(1/4)
x = +/-(1/2)

Since point C is towards point B, we have to take the negative answer:
x = -(1/2)

- Therefore the correct answer is C: -0.5

Shannon collects charms for her charm bracelet. her charm bracelet had 4 charms when she bought it. each year on her vacation she buys 2 more charms to add to her bracelet. assume that shannon continues to buy the same number of charms each year. write an equation that can be used to find how many charms shannon will have on her bracelet after 5 years.

Answers

I think it should be y=4+2*5

2x + 4 = the number of charms that Shannon has

x = the number of years that Shannon has had the bracelet

Replace x with 5 to find the total number of charms after 5 years

2*5 + 4 = 14 charms after 5 years.

Which ordered pair is the best estimate for the solution of the system of equations?

y=âˆ’34xâˆ’2y=x+6

(âˆ’4.25,1.5)

(âˆ’4.75,1.75)

(âˆ’4.5,1.5)

(âˆ’4.5,1.75)

Answers

Final answer:

The best estimate for the solution of the system of equations is (-4.5, 1.5).

Explanation:

The system of equations given is:

y = -34x - 2

y = x + 6

To find the best estimate for the solution, we can substitute the x-coordinate from each ordered pair into the second equation and solve for y.

Let's check each option:

For (-4.25, 1.5):

1.5 = -4.25 + 6

1.5 = 1.75 (not equal)

This is not a solution for the system.

For (-4.75, 1.75):

1.75 = -4.75 + 6

1.75 = 1.25 (not equal)

This is not a solution for the system.

For (-4.5, 1.5):

1.5 = -4.5 + 6

1.5 = 1.5 (equal)

This is a solution for the system.

For (-4.5, 1.75):

1.75 = -4.5 + 6

1.75 = 1.5 (not equal)

This is not a solution for the system.

Therefore, the best estimate for the solution of the system of equations is (-4.5, 1.5).

what is y−4=−2(x+7) written in standard form?

Answers

y=2x+18

Hope that helps!

The standard form of a linear equation is [tex]ax+by=c[/tex], where a, b, and c are numbers.

You are given [tex]y-4=-2(x+7)[/tex]. We need to start by expanding and simplifying.

[tex]y-4=-2x-14\\y=-2x-14+4\\2x+y=-10[/tex]

Some teachers, including mine when I took Algebra 1, require that you find integers (whole numbers) for a, b, and c, and that a be positive. Here, we are fine.

Please explain it and tell me how u got the answer
Thx

Answers

The y-intercept of a function is that function's value when x=0.
.. f(0) = 4
.. g(0) = 0
These y-intercepts differ by 4.

If you want them to differ by zero (be the same), you have to move them to the same point.

Selection 1. Moves f(0) down 3 (to 1) and g(0) up 1 (to 1), so moves the y-intercepts to the same point. This is what you want, so this is an appropriate answer selection.

Selection 2. Moves f(0) up 4 (to 8) and g(0) down 1 (to -1). 8 and -1 are not the same point, so this is not the answer.

Selection 3. Moves f(0) down 2 (to 2) and g(0) up 1 (to 1). 2 and 1 are not the same point, so this is not the answer.

Selection 4. Moves f(0) up 3 (to 7) and g(0) down 6 (to -6). 7 and -6 are not the same point, so this is not the answer.

___
The appropriate choice is the 1st one.
  f(x) - 3 and
  g(x) + 1

A roped off area of width x is created around a 4-foot by 6-foot rectangular museum of display of Native American artifacts. The combined area of the display and the roped-off is 120 square feet. Find the width.

Answers

Let
x----------> width a roped off area

we know that
(4+2x)*(6+2x)=120
then
4*6+4*2x+2x*6+2x*2x=120 ---> 24+8x+12x+4x²=120 -------> 4x²+20x+24=120
4x²+20x-96=0

using a graph tool---------> to calculate the quadratic equation
see the attached figure

the solution is
x=3 ft

the answer is
the width a roped off area is 3 ft

The width of the roped off area around the museum display is 4 feet.

To find the width of the roped off area around the museum display of Native American artifacts, we need to solve for x in the area equation. The area of just the display is 4 feet by 6 feet, which is 24 square feet. Since we know the combined area of the display and the roped-off area is 120 square feet, the equation is:

Area of display + Area of roped-off region = Total Area

(4)(6) + ((4 + 2x)(6 + 2x) - (4)(6)) = 120

24 + (24 + 4x + 12x + 4x2) - 24 = 120

Simplifying, we get:

4x² + 16x - 96 = 0

Divide by 4:

x² + 4x - 24 = 0

Factor the quadratic equation:

(x + 6)(x - 4) = 0

Setting each factor equal to zero gives us two potential solutions:

x + 6 = 0
or
x - 4 = 0

Therefore, x can be -6 or 4. Since a width can't be negative, the only logical solution is:

x = 4 feet

The width of the roped-off area is 4 feet.

10 points!
Which graph represents the solution to the system of inequalities?
2x – y ≥ 3
x + 2y < 4

Answers

Graph C is the answer.

2x – y ≥ 3x + 2y < 4
=y is less than or equal to 2x-3
y is less than -x/2+2

Answer:

graph c is the correct answer hope this helps you get an A.

which do you think would seat more people a 4ft by 6 ft rectangular table or a circular table with a diameter of 6 ft? How many people would sit at each table? Explain your reasoning.

Answers

To determine which seating arrangement would be able to seat more people you will find the distance around each table.

For the rectangle, you will find the perimeter:

P = 2l + 2w
2 x 6 + 2 x 4
P = 20 feet

For the circle you will find the circumference:

C = pi x d
3.14 x 6
C = 18.84 feet

The rectangle would seat more people because the distance around the table is longer.

You would be able to fit about 7-8 people around the rectangular table and 6-7 people around the circular table.

Final answer:

Comparing a 4ft by 6ft rectangular table and a circular table with a 6ft diameter, the circular table can seat more people (approximately 9) due to more efficient use of its perimeter, compared to the rectangular table which can seat 6 people.

Explanation:

The question asks which table would seat more people: a 4ft by 6ft rectangular table or a circular table with a diameter of 6ft. To answer this, we need to compare the arrangements and sizes of the two tables.

The rectangular table measures 4 feet by 6 feet. Typically, a person needs about 2 feet of space at a dining table to sit comfortably. Therefore, on the longer sides (6 feet), you can seat 3 people on each side, for a total of 6. On the shorter sides (4 feet), it's not practical to seat anyone due to space constraints and leg room. So, the rectangular table can seat 6 people.

The circular table has a diameter of 6 feet. Placing chairs around a circle often allows for more efficient use of space. If we assume each person requires the same 2 feet of space, roughly, the circumference of the table (which is π * diameter) dictates how many people can sit around it. The circumference of a 6-foot diameter table is about 18.85 feet (π * 6). Dividing this by 2 feet per person, you can seat approximately 9 people around the circular table.

In conclusion, a circular table with a diameter of 6 ft would seat more people, approximately 9, compared to a 4ft by 6ft rectangular table, which would seat 6 people. This is due to the circular table's ability to more efficiently use the perimeter for seating.

Ben walks at a rate of 3 miles per hour. he runs at a rate of 6 miles per hour. in one week, the combined distance that he walks and runs is 210 miles.
b. (using 3x + 6y = 210 with x representing walk and y representing run) ben runs for 25 hours. for how many hours does he walk?

Answers

25 x 6 is 150 out of 210 miles therefore Ben ran for 150 miles and walked for 60 miles

The explicit rule for a sequence is an=14-9n
What is the recursive rule for the sequence?

Answers

you have to add it then divide it

The explicit rule for the sequence is [tex] a_{n}=14-9n [/tex]

Let us put n=1, we get

[tex] a_{1}=14-(9 \times 1)=5 [/tex]

Now let n=2,

[tex] a_{2}=14-(9 \times 2)=-4 [/tex]

Let n=3,

[tex] a_{3}=14-(9 \times 3)=-13 [/tex]

Similarly, in this manner we obtain a sequence as

5, -4, -13, -22,.....

Since we can clearly observe that the first term is '5' and common difference is '-9'.

So, we get recursive rule for the sequence as:

[tex] a_{n}=a_{n-1}-9 [/tex] , where [tex] a_{1}=5 [/tex].

Justin lives in saint paul and goes to school in minneapolis. in the morning, he has 333 transportation options (bus, cab, or train) to school, and in the evening he has the same 333 choices for his trip home. if justin randomly chooses his ride in the morning and in the evening, what is the probability that he'll use both the bus and the train?

Answers

To answer this question you will multiply the probability of the first event happening by the probability of the second event happening. He has a one in three chance of taking the bus on the way to school, and a one in three chance of taking the train home. 1/3 x 1/3= 1/9 chance of both of these occurring at the time he is indicating.

Answer:

2/9

Step-by-step explanation:

TRUST ME THIS GUY ABOVE ME IS A DING DONG

How to find x in this math problem?

Answers

In a triangle, the three interior angles always add to 180° ⇒
The third interior angle of the triangle = 180 - (30+20) = 130°

Vertical angles are equal ⇒ x = 130°

The answer is 130°

Which fraction is NOT equivalent to 8 1/2 ? A) 2 3 B) 24 36 C) 4 6 D) 6 10

What is 5 x 2/3?

A) 3 1/3

B) 3 2/5

C) 5 2/3

D) 10/15

Answers

None of the fractions are equivalent on the first one.

The answer for the second question is A. 3 1/3. 5/1 x 2/3 =10/3 10/3=3 1/3

Will mark brainliest ⭐️⭐️⭐️⭐️⭐️

Answers

is a hope this helped

Answer:

answer is d

Step-by-step explanation:

Rico is making 4 batches of salsa.EAxh batch needs 2/3 cup of corn.He only had a 1/3 cup measure.How many times must rico measure 1/3 cup of corn to have enough for all of the salsa

Answers

He would need to measure the 1/3 cup of corn 2 times

How do you decide which variable to isolate in order to use the substitution method to solve a system of linear equations?

Answers

Find a variable with no coefficient.If there is more than one variable with no coefficient,it dose not matter which one you isolate.Isolate the variable and then use substitution to solve the system of equations.

The way to decide which variable to isolate in order to use the substitution method to solve a system of linear equations is;

to look for the variable with no coefficient or least coefficient and then isolate it and use substitution to solve the simultaneous equation.

A system of linear equations can be solved by three major methods which are;

- Elimination method

- Substitution method

- Graph method

Now, in this question we want to know how substitution method is done.

Let us say we have two simultaneous equations which are;

2x + 3y = 8 ----(eq 1)

x + 5y = 11 ----(eq 2)

Now, in this method, we need to first isolate a variable in one of the equations by making it the subject of formula there. Usually, we go with the variable that has no coefficient first.

In this case, it is x that has no coefficient in eq 2 and as such, we will isolate it to get;

x = 11 - 5y

In conclusion, the way we decide which variable to isolate in substitution method of simultaneous equations is to look for the variable with no coefficient or least coefficient.

Read more at;https://brainly.com/question/19770914

Triangle ABC and Triangle DEF are similar. For triangle ABC, AB = 2x , AC = 24 inches and BC = 20. For triangle DEF, EF = 5 and DF = x - 2 . What is the value of x?

Answers

x=8.

Following the similarity statement, we know that AC is to DF as BC is to EF. The ratio would be:

24/(x-2) = 20/5

Cross multiply:
24*5 = 20(x-2)

Use the distributive property:
120 = 20x - 40

Add 40 to both sides:
120+40 = 20x - 40 + 40
160 = 20x

Divide both sides by 20:
160/20 = 20x/20
8 = x

A $50,000 investment earns 18% annually. If B represents the balance and t represents the number of years, determine an expression that gives the account balance, B, after t years. Also, determine an equivalent expression that displays the effective monthly interest rate.

Answers

Using the compound interest formula;
FV=P(1+r/100)^t

FV is the future value
P is the principle
r is the rate
t is the time

the formula that gives the account balance after t years will be:

FV=50000(1+18/100)^t
FV=50000(1.18)^t

The formula for effective monthly interest rate will be:
monthly interest rate=(annual rate)/(number of months)
annual rate=18%
number of months in a year=12 months
rate=18/12=1.5%

Answer:

usa test prep its B

Step-by-step explanation:

What context clue in the paragraph best helps in understanding the meaning of the word native?

Question 2 options:

"much in America"

"lived in Nantes, France"

"first in France"

"born in Louisiana"

Answers

What was the Answer?

75 less than twice a number

Answers

I think the number is 75 because 75 x 2 = 150 - 75 = 75.

Perform the indicated operation. (r + s)(r2 - rs + s2)

Answers

Final answer:

The operation in the equation, (r + s)(r2 - rs + s2), is solved by distributing the multiplication of the binomial across each term in the trinomial. When the multiplications are complete and the terms are added, the resulting solution is r3 + s3.

Explanation:

The indicated operation in the question is the multiplication of the binomial, (r + s), and the trinomial, (r2 - rs + s2). This can be performed by using the distributed property of multiplication over addition. In this case, you would multiply each term in the binomial by each term in the trinomial, then add the products. So the solution will be:

r3 - r2s + rs2 + r2s - rs2 + s3 = r3 + s3

Note: the terms -r2s and r2s cancel each other out, as do the terms rs2 and -rs2, which is why the final result is r3 + s3.

Learn more about Polynomial Multiplication here:

https://brainly.com/question/20121808

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Suppose that a system has 5000 grasshoppers. how many hawks would be expected?

Answers

Probably 2500 or less because they dont need that much hawks.

What is 5% in a decimal and a fraction?

Answers

5/100 or .05 would be the answers I believe.

It can be helpful to understand that the "%" is a sort of fancy or short-hand way to write "/100".

That is, 5% means 5/100. This is your fraction. It can be reduced to 1/20.

As a decimal, of course, 5/100 = .05, a number with 5 in the hundredths place.

Find the zeros of the function. f(x)=9x^2-12x-5

Answers

x=5/3, -1/3

You can use the quadratic formula or you can do any method that your teacher teaches you (box, etc.)

Answer: 5/3 and - 1/3

Explanation:

1) Set the given function equal to 0: 9x^2 - 12x - 5 = 0

2) make 9x^2 = (3x)^2 and 12x = 4(3x)

=> (3x)^2 - 4(3x) - 5 = 0

3) Factor the polynomial:

(3x - )(3x + ) first stept of factoring.

Now find two numbers that sum - 4 and their product of - 5, those are -5 and + 1: =>

(3x - 5) (3x + 1) = 0

4) Set the two factors equal to 0:

3x - 5 = 0 => 3x = 5 => x = 5/3 ↔ one root

3x + 1 = 0 => 3x = - 1 => x = - 1/3 ↔ the other root.

If the state sales tax is 6% and a city adds an additional 1 1/4% tax,
What will the tax be on a purchase of $146.00? (Round the answer to the nearest cent.)

A. $10.59
B. $8.76
C. $10.80
D. $18.25

Answers

Your answer is A. 10.59 is the tax.

Please answer this and thank you

If DE=4x+10, EF=2-1, and DF=9x-15, find DF.

Answers

I hope that 2-1 means 21.

DE + EF = DF
4x + 10 + 21 = 9x - 15
4x + 31 = 9x - 15
31 = 9x - 4x - 15
31 = 5x - 15
46 = 5x
x = 9 1/5 = 9.2

You want 9x - 15
9*9.2 - 15
82.8 - 15
67.8 <<<<< answer.
If I have given the wrong meaning to 2-1 (which could mean 1) leave another note and I will correct my work.

What is the best first step in solving the equation 3 +3 square root 6x = 5? A.)Subtract 3 from both sides.
B.)Find the cube of 3 square root 6x .
C.)Cube both sides of the equation.
D.) Subtract 5 from both sides.

Answers

Final answer:

The best initial step in solving the equation 3 + 3√(6x) = 5 is to subtract 3 from both sides, simplifying the equation to 3√(6x) = 2, which lays a clear path towards isolating and solving for x.So,option A.)Subtract 3 from both sides. is correct.

Explanation:

The best first step in solving the equation 3 + 3√(6x) = 5 is to simplify the equation by isolating the square root term. This can be done by following option A: Subtract 3 from both sides of the equation. This action makes the equation easier to manage step-by-step as you move toward isolating x, which is the ultimate goal of solving for x. The resulting equation after subtracting 3 from both sides is 3√(6x) = 2. This simplified equation can then be further manipulated to solve for x, primarily by squaring both sides to eliminate the square root, and then solving the resulting simple algebraic equation.

Find the simple interest. $7,064 at 6.5% for 8 months

Answers

the answer is 57.395

Simple Interest can be calculated using the formula I=Pr t

Here I= interest earned ,P= Principal ,R= rate of interest ,t= time in years.

It is given Principal P=$7,064

Rate r=6.5% =0.065

Time t= 8 months =[tex] \frac{8}{12} =\frac{2}{3} [/tex] years

Substituting these values in I = P r t

I =(7064)(0.065)([tex] \frac{2}{3} [/tex])

Solving for I

I=306.11

interest earned on $7,064 at 6.5% for 8 months is $306.11

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