SOLUTION: How do I solve 5^x=1/125?

Question 589185: How do I solve
5^x=1/125?

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
How do I solve
5^x=1/125?
------------
If you recognize that 125 = 5^3, then 5^(-3) = 1/125
--> x = -3
---------------
If not,
x*log(5) = log(1/125)
x = log(1/125)/log(5)
x = -3
-------
If it's a random number, eg, 5^x = 1/126 then you have to use the 2nd method.

RELATED QUESTIONS
How do I solve log base of 125... (answered by josmiceli)

how do I evaluate: Log1/5... (answered by lwsshak3)

Solve... (answered by Theo)

Hi, how do you solve log 5^2x = log... (answered by MathLover1)

How do you solve 4x2=96, x2-20=0, and... (answered by funmath)

How do I write this as a logarithmic equation?... (answered by Alan3354)

How do I solve for x and end up with the correct set? Please give me detailed step by... (answered by stanbon)

How do I solve the exponential equation by expressing each side as a power of the same... (answered by Alan3354)

How would I solve this? 5^x-2 = 125 Any help would be appreciated!... (answered by lwsshak3)