SOLUTION: Please help me solve the problem: {{{ logx8=-3 }}} the x is the number i am looking for. but the x is not really next to the log it is under

Question 257364: Please help me solve the problem:
the x is the number i am looking for. but the x is not really next to the log it is under
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
We can rewrite in exponential form as

Now express 8 as a prime to a power as

But we want the exponents the same so we can rewrite as

cancel the exponents and we have
x = 1/2.
RELATED QUESTIONS
I am trying to solve log(x-1)+log(x+2)=1, I have the answer, which is 3, but am looking... (answered by jim_thompson5910,CharlesG2)

I tried this problem, but the answer that I got doesn't seem right to me. Any help would... (answered by Earlsdon)

Hello my name is Karla I am from the 9th grade I am really stuck on this problem.... (answered by Theo,ikleyn,greenestamps)

I am looking for the inverse of the function y= 3x -1, where x is the power. So it is... (answered by ichudov)

The directions for the problem is "Solve each equation for x to three significant digits� (answered by fractalier)

please help me solve log base 6 X + log base 6 X-3=2 the answer is 7.365 but I need... (answered by lwsshak3)

I have apparently become to reliant on my calculator. I am not sure how to show the work... (answered by ankor@dixie-net.com)

I am not understanding how to solve for x in a matrix. The problem I am looking at is:... (answered by Alan3354)

Hello and I am looking for some help. I need to express this in expanded form if... (answered by ankor@dixie-net.com)