# Exponential Equation

• May 31st 2011, 06:37 PM
kpatch60
Exponential Equation
I was given 3^x-1= 1/9
I took the log of both and got log3*x-1=log(1/9)
At this point I know I have to divide log(1/9)by log(3) to isolate the x but I do not know how to do this without a calculator. Is there a way to do this problem without a calculator?
• May 31st 2011, 06:41 PM
Chris L T521
Quote:

Originally Posted by kpatch60
I was given 3^x-1= 1/9
I took the log of both and got log3*x-1=log(1/9)
At this point I know I have to divide log(1/9)by log(3) to isolate the x but I do not know how to do this without a calculator. Is there a way to do this problem without a calculator?

Spoiler:
Hint: $\log(1/9) = -2\log 3$
• May 31st 2011, 06:44 PM
kpatch60
So just rewrite as 3^-2 and move the exponent to the front position? Thanks, I never looked at it like that.
• May 31st 2011, 06:45 PM
Ackbeet
Do you mean

$3^{x-1}=\frac{1}{9},$ or

$3^{x}-1=\frac{1}{9}?$