Mike is working on solving the exponential equation 74^x = 37; however, he is not quite sure where to start. Using complete sentences, describe to Mike how to solve this equation.

Answers

Answer 1

Answer:

Method 1

[tex]74^x = 37[/tex]

Take natural logs of both sides:

[tex]\implies \ln74^x = \ln37[/tex]

Apply the log power rule: [tex]\ln(a)^b=b \ln (a)[/tex]

[tex]\implies x\ln74 = \ln37[/tex]

Divide both sides by ln 74:

[tex]\implies \dfrac{x\ln74}{\ln74} = \dfrac{\ln37}{\ln74}[/tex]

[tex]\implies x= \dfrac{\ln37}{\ln74}[/tex]

[tex]\implies x=0.8389552282...[/tex]

Method 1

[tex]74^x = 37[/tex]

Take logs of base 74 of both sides:

[tex]\implies \log_{74}74^x = \log_{74}37[/tex]

Apply the log power rule: [tex]\log_am^n=n\log_am[/tex]

[tex]\implies x\log_{74}74= \log_{74}37[/tex]

Apply log of the same number as base rule: [tex]\log_aa=1[/tex]

[tex]\implies x= \log_{74}37[/tex]

[tex]\implies x=0.8389552282...[/tex]

Answer 2

Answer:

[tex]x = \log_{74}(37) [/tex]

Step-by-step explanation:

we want to solve the following exponential equation:

[tex] \iff {74}^{x} = 37[/tex]

Taking common logarithm of both sides yields:

[tex]\iff \log{74}^{x} = \log37[/tex]

recall that,

[tex] log( {a}^{x} ) = x log(a) [/tex]

utilizing it yields:

[tex] \iff x \cdot\log{74} = \log37[/tex]

divide both sides by log74:

[tex]\iff \dfrac{ x \cdot\log{74}}{ \log(74)} = \dfrac{ \log37}{ \log(74) }[/tex]

remember that,

[tex] log_b( {a} ) = \frac{log(a)}{log(b)} [/tex]

hence,

[tex]x = \boxed{ \log_{74}(37)} [/tex]


Related Questions

Easy math pls help quick will give brainlest

Answers

Answer:Easy math pls help quick will give brainlest

Easy math pls help quick will give brainlest

Easy math pls help quick will give brainlestStep-by-step explanation:

is your correct answer

What is the sum of the interior angles of this pentagon?

Answers

Answer:

[tex]sum\ or\ interior\ angles[/tex]

[tex]ol\ pentagon\ is\ 540\textdegree.[/tex]

Step-by-step explanation:

[tex]Given\ of\ Pentagon[/tex]

[tex]To\ hind\ o\ sum\ of\ Interiur\ angle\ of[/tex]

[tex]pentagon.[/tex]

[tex]solutiono[/tex]

[tex]sum\ of\ the\ interior[/tex][tex]angler\ of\ a\ pentajon[/tex]

[tex]can\ be\ round\ by\ 1\ st[/tex]

[tex]dividing\ it\ into\ triangler[/tex]

[tex]from\ 1\ verter.[/tex]

[tex]\therefore\ There\ are\ 3\ Triangles\ made.[/tex]

[tex]sum\ of\ interiar\ angler\ or\ Triangles\ is[/tex]

[tex]180\textdegree.\ Tmere\ are\ 3\ Triangles.[/tex]

[tex]\therefore \ \ \ \ \ 180\times 3=540\textdegree.[/tex]

[tex]Hence\ sum\ ot\ interior\ angles[/tex]

[tex]ol\ pentagon\ is\ 540\textdegree.[/tex]

I hope this helps you

:)

4/8 - 3/10 pa answer ulii

Answers

Answer:

1/5

Step-by-step explanation:

4/8-3/10=1/5

So basically 4/8 -3/10 you first cross multiple the denominators so 8 multiplied by 10 and 3 and 10 multiplied by 8 and 4 so we have a total of 80 which is our denominator and 40-24 which will give us 16/80 then we simplify until we get 1/5 it’s a long way but very easy to understand

From the product of 3y and y^2 -4y +10, subtract y^3 + 7y2 -2y





Please help this is due tonight!

Answers

(3y)(y^2-4y +10) -(y^3 + 7y^2 -2y)
= 3y^3 -12y^2 + 30y - y^3 -7y^2 + 2y
= 2y^3 -19y^2 +32y,,

Hope I can help you!


The length of a rectangle is three feet less than twice its width. Ifx represents the width of the rectangle, in
feet, which inequality represents the area of the rectangle that is at most 30 square feet?
O x(3 - 2.c) < 30
O <(2x - 3) < 30
O 2(3 – 23) > 30
O x(2x - 3) > 30

Answers

x(2x - 3) > 30

hope it helps...!!!

PLEASE HELP ME IM LOSIN ALOT OF POINTS

Answers

Lol I have no ideaaa sorry

Select the best answer for the question.
7. What is 7/4 as a mixed number?
O A. 3/4
O B. 1914
O C. 1314
O D. 11/4

Answers

Answer:

[tex] 1 \frac{3}{4} [/tex]

Step-by-step explanation:

7/4 = [tex] \sf 1 \bold{R} 3 [/tex]

⇢ [tex] 1 \frac{3}{4} [/tex]

Brainleist
help pls
10 points

Answers

Answer:

[tex]m \angle A = 100 \degree[/tex]

Step-by-step explanation:

Given:

[tex]m \angle A= (x-60) \degree \\ m \angle B= (x-40) \degree \\ m \angle C= 130\degree \\ m \angle D= 120\degree \\ m \angle E= 110\degree \\ m \angle F= (x-20) \degree[/tex]

Also, the given diagram is a perfect hexagon, having sum of all interior angles 720°

To find:

[tex]m \angle A= ?[/tex]

Solution:

[tex] \sf \: Sum \: of \: all \: interior \: angles = 720 \degree \\ \sf \: m \angle A + m \angle B + m \angle C + m \angle D + m \angle E + m \angle F = 720 \degree\\ \sf \: (x - 60) + (x - 40) +130 + 120 + 110 + (x - 20) = 720 \degree \\ \sf \: 3x - 120 + 120 + 240 = 720 \\ \sf 3x - \cancel{120}+ \cancel{120} + 240 = 720 \\ \sf 3x = 720 - 240 \\ \sf 3x = 480 \\ \sf x = \frac{480}{3} \\ \fbox{\sf x = 160 \degree}[/tex]

Substituting the value of x in,

[tex]m \angle A= (x-60) \degree \\ m \angle A= 160-60 \\ m \angle A = 100 \degree[/tex]

Thanks for joining brainly community!

Answer:

the answer is 100

Step-by-step explanation:

Ryan is working on his first budget. He has placed all of the fixed expenses on the budget shown and then would like to use the information to evaluate his variable expenses. Ryan's take-home pay is 2,500 each month. Complete the table below the answer the questions below.
please help me
complete the table and answer the four questions below if you tell me how to do I'll be happy to mark you brainlest!!!

1) what percent of his monthly budget do his transport costs account for?

2) what percent of his monthly budget has he accounted for?

3) Ryan would like to save 10% of his take-home pay towards retirement. How much would he be able to save each month?
4) Assume that Ryan does save 10% for retirement. If he allocates the remainder of his take-home pay to entertainment compromise of the total monthly budget? How much will be budgeted towards entertainment?

Answers

The percent of his monthly budget that his transport costs account for will be 17.8%.

How to calculate the percentage?

The percent of his monthly budget that his transport costs account for will be:

= 325/(800 + 450 + 125 + 325 + 125) × 100

= 325/1825 × 100

= 17.8%

The percent of his monthly budget has he accounted for will be:

= 1825/2500 × 100

= 73%

When he saves 10% of his take-home pay towards retirement, the amount saved will be:

= 10% × $2500

= $250

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The percent of Rayan's monthly budget that his transport costs account for will be 17.8%.

1. The proportion of his monthly budget that his transit expenses make up is:

= 325/(800 + 450 + 125 + 325 + 125) × 100

= 325/1825 × 100

= 17.8%

The proportion of his monthly budget that he has already accounted for is:

= 1825/2500 × 100

= 73%

He will save the following sum for retirement if he sets aside 10% of his after-tax income:

= 10% × $2500

= $250

The answer is $250.

2. To find the percentage of his monthly budget accounted for by transport costs, we add up the amounts for Car Payment and Gas:

$325 + $125 = $450.

Then we calculate the percentage: (450 / 2500) x 100% = 18%. Therefore, his transport costs account for 18% of his monthly budget.

3. To find the percentage of his monthly budget accounted for overall, we sum up all the amounts in the table:

$800 + $450 + $125 + $325 + $125 = $1,825.

Then we calculate the percentage: (1825 / 2500) x 100% = 73%. Therefore, he has accounted for 73% of his monthly budget.

4. To calculate how much Ryan can save each month for retirement, we take 10% of his take-home pay:

10% of $2,500 = $250.

Thus, he can save $250 each month for retirement.

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#SPJ6

A point with a coordianates plane (-c -d) is shown on the coordinate grid

Answers

Ans The answer to the question is ###404 bad gateway Step-by-step explanation:

help plsssssssssssssssssssssssssssssssss

Answers

Answer:

I guess it is $105.Not so sure about my answer...

what numbers multiplied gives you -70 but added gives you -33

Answers

Answer:

-35, 2

Step-by-step explanation:

When you multiply -35*2 you will get -70

When you add a positive number to a negative number you will take the larger number and if it is negative you will add the positive and if it is positive you take away negative so -35+2 will be -33

Explain why this comparison is either reasonable or not reasonable. 7.52 > 7.5​

Answers

Answer:

Step-by-step explanation:

7.52 is greater than 7.5 because 7.52 has 2 hundredths more value as 7.5 is only 7.50.

Given the function f(x) = 2x2 - 27, find f(h +2).

Answers

Answer:

f(h + 2) = 2h² +8h - 19

Step-by-step explanation:

f(x) = 2x² - 27

f(h + 2) = 2(h + 2)² - 27

f(h + 2) = 2(h²+4h+4) - 27

f(h + 2) = 2h² + 8h + 8 - 27

f(h + 2) = 2h² +8h - 19

I hope this helps!

what is the least common denominater of 1/2, 2/3, and 3/8?

Answers

Answer:

24

Step-by-step explanation:

2×12 =24

3×8 =24

8×3 =24

PLEASE HELP WILL MARK BRAINLIEST!!!

Which fraction has a value that's equal to 3/4?
A. 12/12
B.4/3
C. 12/16
D. 9/16

Answers

Answer:

C. 12/16

Step-by-step explanation:

If you multiply both the numerator AND the denominator by four you end up with the equivalent fraction of 12/16.


What is the value of x in the proportion below?
5/60=8/x

Answers

Answer:

x = 96

Step-by-step explanation:

5 = 8

__ __

60 x

*do cross multiply

5x = 8x60

5x = 480

x = 480/5

x = 96

Find an equation of the ellipse that has center (2,0), a major axis of length 12, and endpoint of minor axis (5,0).

Answers

The standard formula of the ellipse with center (2, 0), a major axis of length 12 and endpoint of minor axis (5, 0) described in the statement is (x-2)²/9 + y²/36 = 1.

How to derive the equation of the ellipse based on given information

The ellipse is a kind of conic whose formula in standard form is shown below:

(x-h)²/b²+(y-k)²/a² = 1     (1)

Where:

x, y - Orthogonal axes of the ellipse.h, k - Location of center of the ellipse.b - Length of the minor semiaxis.a - Length of the major semiaxis.

In this question we are supposed to construct the standard equation the ellipse by replacing all the variables. If we know that b = 3, a = 6, h = 2 and k = 0, then the standard equation of the ellipse is:

(x-2)²/9 + y²/36 = 1     (2)

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in the blanks below. Find the slope of the line passing through the points (-9, 2) and (9,2). slope: ​

Answers

I will assume that we are trying to find the slope between (-9,2) and (9, 2)

The slope's equation ⇒  [tex]\frac{y2-y1}{x2-x1}[/tex]

Let's set the variables:

   (x1, y1) --> (-9, 2)

   (x2, y2) --> (9, 2)

Now let's plug them in:

  [tex]Slope = \frac{2-2}{9--9} =\frac{0}{18} =0[/tex]

Thus the slope of the line is 0.

Hope that helps!

What is the five-number summary of this data set?

{403, 276, 649, 786, 274, 189, 654, 652, 572}

Drag the numbers into the boxes to correctly complete the five-number summary.
Minimum
Q1
Q2
Q3
Maximum
(choices)
189 274 275 276 572 652 653 654 786

Answers

Answer:

Minimum: 189

Q1: 275

Q2: 572

Q3: 653

Maximum: 786

Step-by-step explanation:

I took the test, I got it wrong but I looked back at the answer I hope this helped. And I am sorry this is late.

Answer:

Minimum: 189

Q1: 275

Q2: 572

Q3: 653

Maximum: 786

Step-by-step explanation:

I took the test, I got it wrong but I looked back at the answer I hope this helped. And I am sorry this is

plsssssssss helpppppppppppppppppppp

Answers

Answer:

#1 B  inferential

#2 A descriptive

Step-by-step explanation:

Hope this helps!

Write Down 3 numbers where the following are true:the total of the three numbers is 20.The product of the three numbers is 90

Answers

Answer:

1, 9 and 10.

Step-by-step explanation:

Let the 3 numbers be x, y  and z, then

x + y + z = 20

xyz = 90

Assuming the numbers are whole numbers lets find the prime factors of 90:

90 = 2*3*3*5

So we need to combine these factors to fit the 2 eqautions.

Now 90 = 9 * 10

= 1 * 9 * 10

If we include 1 as one of the 3 numbers then 1, 9 and 10 will fit the bill.

Answer 1, 9 and 10

Find the next two terms in this sequence.

50,40,31,23,16,[???][???]

Answers

Answer:

10, 5.

Step-by-step explanation:

The differences are -10, -9, -8, -7,

so the next 2 terms are 16-6 and 10 - 5

= 10, 5


Which statement is true?
• A.
A sample statistic can never be equal to the population parameter.
O B. Point estimates are defined for both samples and populations.
O C.
To calculate a sample proportion, we
need to know the population size
O D.
To calculate a point estimate, we
need to know the sample size.

Answers

Answer: Choice D

To calculate a point estimate, we need to know the sample size.

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

Explanation:

Let's go through the answer choices.

A) False. A sample statistic could equal to the population parameter. It won't always happen, but it might happen sometimes (in rare cases). B) False. Point estimates are only defined for populations. They estimate a population parameter. For example, the sample mean xbar is a point estimate of the population mean (mu).C) False. In practice, we will hardly know anything about the population. This includes the population size. The goal of statistics is to measure population parameters by using sample statistics as estimation methods.D) True. We can easily calculate the sample size because it is relatively much smaller compared to the population. Plus, when selecting the sample, the sample size is often pre-determined to some set number. The sample size will help us determine things like the sample mean and the sample proportion.

The math club needs to raise at least $552.50 for a trip to state
competition. The club has raised 12% of the funds. Members want
to find out how much they each need to raise to make up the
difference.

Which inequality shows how much money each of the 7
club members need to raise if each member raises the same
amount?

A. m < $69.46
B. m > $69.46
C. m < $72.35
D. m > $72.35

Answers

ok so they raised 12%

12%=12/100=0.12

12% of 552.5=.12 times 552.5=66.3 was raised

552.5-66.3=486.2

divide by 7

486.2/7=69.457 about 69.46

each member must raise at least 69.46

Prism X is a dilation of Prism Y. The height of Prism X is 10 1/3 ft, and the volume of Prism X is 74 2/5 ft³. The height of Prism Y is 5 1/6 ft.

What is the volume of Prism Y?

Enter your answer as a mixed number in simplest form by filling in the boxes.

Answers

Answer:

The volume of Prism Y which is dilated to form prism X is 981 1/3 ft³

how do I find the area of composite figures​

Answers

The area of the composite figure involving rectangle and trapezium is 810.5cm².

How to calculate the area?

The area can be found by adding the area of the rectangle and trapezium. This goes thus:

Area of rectangle = Length × Width = 15 × 23 = 345cm²

Area of trapezium = 1/2(a + b)h

= 1/2(15 + 34) × 19

= 1/2 × 49 × 19

= 465.5cm²

The area will now be:

= 345cm² + 465.5cm²

= 810.5cm²

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julia has 3/4 quart of ice cream. She gives 3/7 of it to her sister. How many quarts of ice cream does JULIA HAVELEFT?

Answers

9/28
3/4 = 21/28
4/7= 12/29
21-12=9
9/28

given the following cofunction sin(x - 3)° = cos(2x + 6)°, what is the measure of the smaller angle

Answers

Note :

sin(x) = cos (90-x)

Therefore,

sin(x-3) = cos(90-(x-3))

90-[x-3] = 2x+6

90-x+3 = 2x+6

3x = 93-6

x = 31-2

x = 29°

what digit is in the one thousands place in 419,287​

Answers

Answer:

9

Hope This Helps! :)

Answer:

9 is in the thousands place.

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