Question

Wendell is looking over some data regarding the strength, measured in Pascals (Pa), of some building materials and how the strength relates to the length. The data are represented by the exponential function f(x) = 2^x, where x is the length. Explain how he can convert this equation to a logarithmic function when strength is 8 Pascals.

Answer 1

I got x = log_2 8

Answer 2

@campbell_st

Answer 3

well you can take the log of both sides

and use the log law for powers

\[\log(a^b) = b \times \log(a)\]

and you should recognise

\[8 = 2^3\]

so

\[\log(2^x) = \log(2^3)\]

now use the log law above...

Answer 4

So the answer is 3 x log(2)?

Answer 5

well you need to solve for x so

xlog(2) = 3log(2)

divide both sides of the equation by log(2) and you get

x = 3

the question doesn't need logs... it just needs the skill of identifying 8 as 2^3

hope it helps

Answer 6

Do I need to solve for x? Doesn't the question just ask to convert the equation to a log function?

Answer 7

I think the answer must be in the form x = log_b y.

Answer 8

@sleepyjess

Answer 9

@JoannaBlackwelder

Answer 10

I agree with your answer :-)

Answer 11

Thanks. Could you explain why?

Answer 12

We plug in 8 for f(x) since that is the Pascals.

Answer 13

Then solve for x using the rules of logs.

Answer 14

But I agree that it would simplify to 3

Answer 15

log_2 8 = 3, so it is just a simplification

Answer 16

Sorry, i meant since 8 = 2^3, does the answer change?

Answer 17

Sorry, I'm not sure what you mean.

Answer 18

Well, I was saying that x=log_2 8 which simplifies to x=3

Answer 19

Are you sure the answer is log_2 8 = 3?

Answer 20

No

Answer 21

Okay, well I think that your explanations made a lot of sense, so I will just go with that. Thanks for your time and patience!

Answer 22

Ok, you're welcome