202,000=32,800e^k*20 - Solve for K

[killersanta]

Homework Statement

Did most the problem, but know I'm stuck here: 202,000=32,800e^k*20

I need to solve for K

The Attempt at a Solution

Log 202,000 = k*20 log 32,000 e

Do you move the e out in front too? I'm not sure, anyway, I'm stuck here. Not sure what to do or even if you use logs to solve for k.

 

[berkeman]

Homework Statement

Did most the problem, but know I'm stuck here: 202,000=32,800e^k*20

I need to solve for K

The Attempt at a Solution

Log 202,000 = k*20 log 32,000 e

Do you move the e out in front too? I'm not sure, anyway, I'm stuck here. Not sure what to do or even if you use logs to solve for k.

Remember to use "ln" and not "log" for the inverse operation of $$e^x$$

So if you isolate the $$e^x$$ term, it looks more like this:

$$\frac{202000}{32800} = e^{k*20}$$

What would you now do to get rid of the exponential issue so you can deal directly with k?

BTW, I assume this is the end of a calculus problem, with the end not involving calculus.

 

[killersanta]

Remember to use "ln" and not "log" for the inverse operation of $$e^x$$

So if you isolate the $$e^x$$ term, it looks more like this:

$$\frac{202000}{32800} = e^{k*20}$$

What would you now do to get rid of the exponential issue so you can deal directly with k?

BTW, I assume this is the end of a calculus problem, with the end not involving calculus.

LN(202,000/32800)= K * 20

k = (LN(202,000/32800)/20) = .09089 ?????

 

[Mark44]

That works for me.

Be advised, though, that most people would read e^k*20

as e^k * 20, and not as e^20k, as I think you intended. To better show your intent, write that part as e^(20k). Then it's clear what is in the exponent.

 

[killersanta]

That works for me.

Be advised, though, that most people would read e^k*20

as e^k * 20, and not as e^20k, as I think you intended. To better show your intent, write that part as e^(20k). Then it's clear what is in the exponent.

Sweet, Thanks.... And I will do from now on.