Use logarithms to solve the equation 5^x = 3^(2x-1), giving your answer correct to 3 significant figures.

Answers

Answer 1

[tex]5^x = 3^{2x-1}\\\\\implies \ln(5^x) = \ln\left(3^{2x-1}\right)\\\\\implies x \ln 5 = (2x-1) \ln 3\\\\\implies x \ln 5 = 2x \ln 3 - \ln 3\\\\\implies 2x \ln 3 - x \ln 5 = \ln 3\\\\\implies x(2 \ln3 - \ln 5) = \ln 3\\\\\implies x =\dfrac{\ln 3}{2 \ln 3 - \ln 5} = 1.87[/tex]

Answer 2

The solution to the equation is x ≈ 1.864 (correct to 3 significant figures).

To solve the equation 5ˣ = 3²ˣ⁻¹ using logarithms, we'll take the logarithm of both sides to bring down the exponent. Since the bases are different (5 and 3), we can use either the natural logarithm (ln) or the common logarithm (log base 10). Let's use the natural logarithm (ln):

Take the natural logarithm (ln) of both sides:

ln(5^x) = ln(3²ˣ⁻¹)

Apply the logarithm rule: ln(a^b) = b * ln(a):

x * ln(5) = (2x - 1) * ln(3)

Expand the equation:

x * ln(5) = 2x * ln(3) - ln(3)

Move the terms with "x" to one side of the equation:

x * ln(5) - 2x * ln(3) = -ln(3)

Factor out "x" from the left side:

x * (ln(5) - 2 * ln(3)) = -ln(3)

Solve for "x":

x = -ln(3) / (ln(5) - 2 * ln(3))

Now, we can calculate the value of "x" using a calculator:

ln(3) ≈ 1.099

ln(5) ≈ 1.609

x ≈ -1.099 / (1.609 - 2 * 1.099) ≈ -1.099 / (1.609 - 2.198) ≈ -1.099 / (-0.589) ≈ 1.864

Therefore, the solution to the equation is x ≈ 1.864 (correct to 3 significant figures).

Learn more about natural logarithm from the link given below.

https://brainly.com/question/29154694

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Related Questions

Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 4 < x < 7.
f(x)
3
5
4.
9
5
15
6
23
7
33
Answer:
Submit Answer
attempt 2 out of 2

Answers

Answer:

  8

Step-by-step explanation:

It appears your table includes points (4, 9) and (7, 33). The average rate of change on the interval is the slope of the line between these two points:

  m = (y2 -y1)/(x2 -x1)

  m = (33 -9)/(7 -4) = 24/3 = 8

The average rate of change is 8.

in hillary's garden, she has 5 variety of snake plants and 15 variety of orchids. what is the ratio of snake plants to orchids?

Answers

Answer:

1:3

Step-by-step explanation:

She has 1 snake plant for every 3 orchids.

x - y = 3
b) Work out the value of 2x – 2y

Answers

Answer: 2x-2y=3
Step-by-step
Explanation:

please help will brain list if correct no links please ​

Answers

Answer:

C

Step-by-step explanation:

the angle opposite of it is 30

How would the expression x3 -3 sqrt 3 be rewritten using difference of cubes?
O A. (x- 13 )(x2-3x - 3)
O B. (x+ 3)(x + 13 x + 3)
C. (x - 13 )(x2 + 3x + 3)
O D. (x- vb)(x2 + v3 x+3)

Answers

Answer:

x^3 - (√3)^3

I'm not so sure since it's not even an option

Step-by-step explanation:

x^3 - 3√3 = x^3 - 3^1 × 3^(1/2)from the laws of indices: 3^1 × 3^(1/2) = 3^(1 + 1/2)= 3^(3/2) which is the same as (√3)^3so it could be written as x^3 - (√3)^3

how do i multiply 4000x by the square root of 42

Answers

Answer:

25922.963

Step-by-step explanation:

the square root of 42 is 6.48074069841

4000*6.48074069841 is 25922.9627936

13*10-20 im in a hurry

Answers

Answer: 110

Step-by-step explanation:

13*10 = 130-20 is 110

The answer: 13 × 10 - 20 = 130 - 20 = 110

OK done. Thank to me :>

PLZ SOLVE THE PROBLEM

Answers

Answer:

[tex]-2\frac{1}{2}[/tex]

Step-by-step explanation:

→ Minus the 2 numbers from each other

[tex]-1\frac{1}{5} -1\frac{3}{10}[/tex]

→ Find the LCM

[tex]-1\frac{2}{10} -1\frac{3}{10}[/tex]

→ Simplify

[tex]-2\frac{5}{10} =-2\frac{1}{2}[/tex]

5(x-a)=3(x+b)

Solve for x

Answers

Answer:

[tex]x=\frac{3b}{2} +\frac{5a}{2}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

5(x - a) = 3(x + b)

5x - 5a = 3x + 3b

      2x = 5a + 3b

        x = 2.5a + 1.5b

On Monday there are 25 pencils in a basket, If 3 pencils are taken out of the basket each day, how many pencils are left in the basket on Friday?

Answers

13 cuz add 4 days then friday so 4×3 which is 12 and 12-25 so ye its 13

Answer this by 4:20 EST and I will mark brainliest

Answers

Answer:

A

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6, a ) and (x₂, y₂ ) = (9, - 4 )

m = [tex]\frac{-4-a}{9-6}[/tex] = [tex]\frac{-4-a}{3}[/tex]

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

2x - 3y = 6 ( subtract 2x from both sides )

- 3y = - 2x + 6 ( divide through by - 3 )

y = [tex]\frac{2}{3}[/tex] x - 2 ← in slope- intercept form

with slope m = [tex]\frac{2}{3}[/tex]

Parallel lines have equal slopes , then

[tex]\frac{-4-a}{3}[/tex] = [tex]\frac{2}{3}[/tex] , so

- 4 - a = 2 ( add 4 to both sides )

-a = 6 ( multiply both sides by - 1 )

a = - 6 → A

Find the difference between the lengths of the longest and shortest sides of a rectangle if its area is 924 square milimetres and its perimeter is 122 milimetres.

Answers

Length =l

Height = h

Area function = l * h = 924

Perimeter function = 2i + 2h = 122

Divide by 2

I + h = 61.

Plug in I or h for the other variable

I * (61 - I) = 924

61i - i^2 = 924

Factor the function

(-I + 28)(I - 33) = 0

l = 33 as l cannot be negative

61 - 33 = 28

h = 28

Difference between h and l is 33-28=5

select the correct product for the problem below. (−85)(23)(−4) =? -64/15 64/15 16/60 -16-60 64-60

Answers

Answer: 7,820

Sorry I have no help :(

Christina has 6 pieces of candy in her lunchbox. Rachel gives Christina more pieces of candy. Now Christina has 18 pieces of candy. How many pieces of candy did Rachel give Christina?

Answers

18 - 6 = 12

When subtracting the new amount by the original amount, you will find the change or the amount that Rachel gave

18 - 6 = 12

So, Rachel gave Christina 12 pieces of candy.

Answer:

18-6=12

She gave her 12 more pieces of candy.

hope this helps.

Find an expression with represents the sum of 5X -8 and 2X +2 in simplest terms

Answers

Solution: 7x-6
Step by step solution:
5x-8+2x+2
Then combine like-terms
5x+2x+2-8
7x-6
Hope that helps :)

Which statements are correct interpretations of this graph?

Select each correct answer.


a.4 boxes are filled every 3 min.

b.3 boxes are filled every 4 min.

c.1.3 boxes are filled per minute.

d.0.75 boxes are filled per minute.

Answers

It’s b. 3 boxes are filled every 4 mins

When a guy says i cheated just to let the world know what does it mean?
Answer ASAP

Answers

Answer:

He says that because he thinks ur cheating for attention. When they say you 'let the whole world know' that you`re unloyal and can be with any guy, without a care, it`s an insult.

Answer:

it means that he was dating another person while already dating

Step-by-step explanation:

it like when ur dating 2 people at one time without the other person knowing

how long did it take for Car A to travel 10 meters

Answers

Answer:

isnt it 5 seconds?

its quite blurry but i think its 5

It took car A five seconds to travel 10 meters. The 5 on the x-axis aligns with the 10 meters on the y-axis.

you have to solve for X

Answers

Answer:

x = 5/8

Step-by-step explanation:

(1/2) / 4 = x / 51 / 8 = x / 5x = 5 / 8
(1/2)/4=x/51/8=x/55=8xx=5/8

Done

Does (–1, 2) make the equation y = x + 9 true?

Answers

Answer:

(-1, 2) does not make the equation y=x+9 true.

Step-by-step explanation:

y=x+9

(-1, 2)=(x, y)

2=(-1)+9,

-1+9=8,

2 does not equal to 8.

Answer: No.

Which one has more kinetic energy water or boiling water

Answers

Answer: 5

Step-by-step explanation:

because idek sorry

The local movie theater, Scene It Cinema, had a special showing of the latest dinosaur movie. There were 6 youth tickets sold for every 5 adult tickets sold.

If there were 70 adult tickets sold, how many movie tickets were sold altogether?

Answers

Answer:

Let the youth and adult tickets be y and x respectively.

6y + 5x ---> (1)

From statement (1):

(1) × 14

84y + 70x

For every 70 adult tickets sold, 84 youth tickets were sold.

Total number of tickets sold= 70 + 84

                                              = 154

A triangle has vertices at A(-3, 2), B(-1, -5) and C(4, 5). The triangle is transformed using the rule ro,o . What are the coordinates of A", B', and C?

Answers

Answer:

I thinck letter c.

Step-by-step explanation:

Because C.

someone help me with this it’s literally easy but i’m still having a hard time to do it

Answers

Answer:

m2= 83 m1=97 m4=83

Step-by-step explanation:

m3 and m1 are corresponding by being verticle so they're the same

m3 and m2 are supple whcih mean they add to 180, so subtract 180-97 which is 83.

m2 and m4 are corresponding by being verticle so they're the same

Let f(x) = x^6( x − 8 )^7 / (x^2 +2)^2
Use logarithmic differentiation to determine the derivative.
f ' (x) =________

Answers

If

f(x) = x⁶ (x - 8)⁷ / (x² + 2)²

then taking the logarithm of both sides lets us expand the right side as

ln(f(x)) = ln(x⁶ (x - 8)⁷ / (x² + 2)²)

ln(f(x)) = ln(x⁶) + ln((x - 8)⁷) - ln((x² + 2)²)

using the property ln(ab) = ln(a) + ln(b).

We can also use the property ln(aⁿ) = n ln(a), so that

ln(f(x)) = 6 ln(x) + 7 ln(x - 8) - 2 ln(x² + 2)

Then differentiating both sides using the chain rule gives

f'(x)/f(x) = 6 x'/x + 7 (x - 8)'/(x - 8) - 2 (x² + 2)'/(x² + 2)

f'(x)/f(x) = 6 (1)/x + 7 (1)/(x - 8) - 2 (2x)/(x² + 2)

f'(x)/f(x) = 6/x + 7/(x - 8) - 4x/(x² + 2)

Solve for f'(x) :

f'(x) = (6/x + 7/(x - 8) - 4x/(x² + 2)) f(x)

and replace f(x) with the given function :

f'(x) = (6/x + 7/(x - 8) - 4x/(x² + 2)) • x⁶ (x - 8)⁷ / (x² + 2)²

We can expand the product :

f'(x) = 6 x⁵ (x - 8)⁷ / (x² + 2)²+ 7x⁶ (x - 8)⁶ / (x² + 2)² - 4x⁷ (x - 8)⁷ / (x² + 2)³

then simplify by factoring :

f'(x) = x⁵ (x - 8)⁶/(x² + 2)³  • (6 (x - 8) (x² + 2) + 7x (x² + 2) - 4x² (x - 8))

Simplify the rest :

f'(x) = x⁵ (x - 8)⁶ (9x³ - 16x² + 26x - 96)/(x² + 2)³

The average playing time of compact discs in a large collection is 35 minutes, and the standard deviation is 5 minutes.
a. What value is 1 standard deviation above the mean? 1 standard deviation below the mean? What values are 2 standard deviations away from the mean?
b. Without assuming anything about the distribution of times, at least what percentage of the times is between 25 and 45 minutes?
c. Without assuming anything about the distribution of times, what can be said about the percentage of times that are either less than 20 minutes or greater than 50 minutes?
d. Assuming that the distribution of times is approximately normal, about what percentage of times are between 25 and 45 minutes? less than 20 minutes or greater than 50 minutes? less than 20 minutes?

Answers

68% are within 30 minutes to 40 minutes, 95% are within 25 minutes to 45 minutes and 99.7% are within 20 minutes to 50 minutes

The three sigma rule states that 68% are within one standard deviation of the mean, 95% are within two standard deviation from the mean and 99.7% are within three standard deviation from the mean.

Given that μ = 35, σ = 5

68% are within one standard deviation = μ ± σ = 35 ± 5 = (30, 40)

95% are within two standard deviation = μ ± 2σ = 35 ± 2*5 = (25, 45)

99.7% are within three standard deviation = μ ± 3σ = 35 ± 3*5 = (20, 50)

`Find out more on three sigma rule at: https://brainly.com/question/25966249

you buy 2.3 pounds of apples for $1.43 per pound. how much do you spend

Answers

Answer:

$3.36

Step-by-step explanation:

$1.43 = 1 lbs

$1.43 + $1.43 = $2.86

$2.86 + .3 = $3.36

the elevation of the salton sea in california is 66 meters below sea level. which integer best represents this elevaton in meters?

please help

Answers

Answer:

-66

Step-by-step explanation:

If we use 0 as the centre of all numbers, and another number is 66 below this baseline, we could say that it is -66 meters above sea level, or 66 meters below sea level.

The perimeter of a rectangle is 20/33 feet. The length of three sides together is 16/33 feet.
What is the length of the fourth side?

40 feet
4/33feet
16/33feet
20/33feet

Answers

Answer:

40 feet

Step-by-step explanation:

on edge

this is long division… please help

Answers

Answer:

23.35

Step-by-step explanation:

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