Question

Convert the given function into a logarithmic function. Please help, I give medals!

Answer 1

F(x) = 3.64e^(0.06x)

Answer 2

We can start by taking the natural log of both sides of the equation.

Answer 3

What is the natural log

Answer 4

The natural logarithm is defined as a logarithim who base is e = 2.718. . .

Answer 5

Okay, so what would we do?

Answer 6

We can let F(x) = y. When we take the natural log of both sides, we have\[\ln (y) = \ln(3.64*e ^{0.06x} )\]

Answer 7

Okay, now what?

Answer 8

Applying logarithim rules, we can split the right hand side of this equation into two natural logs. \[\ln(y) = \ln(3.64) + \ln(e^{0.06x})\]

Answer 9

How do you find the inverse?

Answer 10

We are finding the inverse of the original equation

Answer 11

Okay, so what do we do after In (y) = In(3.64) + In (e^0.06x)

Answer 12

Since ln(x) and e^x are inverses of each other, the right hand side of the equation reduces as follows\[\ln(y) = \ln(3.64) + 0.06x\]

Answer 13

Okay, do I have to reduce In (3.64)

Answer 14

Depends if the answers are in decimal approximations or not. In the end, we solve for x and find that\[x = (50/3)( \ln(y) - \ln(3.64) )\]

Answer 15

Where did 50/3 come from?

Answer 16

from the 0.06. 0.06 = (6/100) = (3 / 50). When we multiply across the equal sign, then we have 50/3.

Answer 17

So what is the logarithm?

Answer 18

What is a logarithm? In general?

Answer 19

The inverse of an exponential function

Answer 20

Right

Answer 21

I need help writing the logarithm

Answer 22

Writing it? The solution for this exercise will be what we established above, where \[x = (50/3)(\ln(y)-\ln(3.64))\] We can further reduces this using log rules and we can write\[x = (50/3) \log(\frac{ y }{ 3.64 })\]

Answer 23

So is that the final answer?

Answer 24

Yes. But where I wrote log, I meant to put ln

Answer 25

Okay so (50/3) In (y/3.64) ?

Answer 26

Yes, x = (50/3)ln(y/3.64)

Answer 27

Okay, thank you :)

Answer 28

Your Welcome. Its really important to know the exponential and logarithm rules for these kind of things. Good luck.

Answer 29

I just have another quick question, what will the graph of this logarithm look like

Answer 30

It looks like this http://www.wolframalpha.com/input/?i=50%2F3+log%28y%2F3.64%29

Answer 31

Okay, thanks :)