Expert: Paul Klarreich - 2/14/2010

Question
Solve the equation: 10e^(3x-7)=100

I've tried simplifying the 100 so that the equation becomes 10e^(3x-7)=10^2, but then I couldn't figure out how to proceed from there.  I also attempted to take the log of both sides, but that didn't appear to give me the correct answer either. Thank you for helping explain this! :-)

Answer
Questioner: Elizabeth
Country: United States
Category: Calculus
Private: Yes
Subject: College Calculus - Logarithmic Functions
Question: Solve the equation: 10e^(3x-7)=100

I've tried simplifying the 100 so that the equation becomes 10e^(3x-7)=10^2, but then I couldn't figure out how to proceed from there.  I also attempted to take the log of both sides, but that didn't appear to give me the correct answer either. Thank you for helping explain this! :-)

........................................
Are you sure it said:

10e^(3x-7)=100  ???

because if it said:

10^(3x-7)=100

then the solution would be fairly simple. (x = 2)

But if it is:

10e^(3x-7)=100

then an obvious simplification is:

e^(3x-7)=10

Then

3x - 7 = ln 10

and  x = (ln 10 + 7)/3

Which is it?