# Thread: Exponential Equation

1. ## 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?

2. 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: $\displaystyle \log(1/9) = -2\log 3$

3. So just rewrite as 3^-2 and move the exponent to the front position? Thanks, I never looked at it like that.

4. Do you mean

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

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