SOLUTION: log(base 125)x - log(base 5)x = -2

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Question 919571: log(base 125)x - log(base 5)x = -2
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
log(base 125)x - log(base 5)x = -2
use change of base formula:

..
log%285%2C%28x%29%29%2F3-log%285%2C%28x%29%29=-2
lcd:3
log%285%2C%28x%29%29-3log%285%2C%28x%29%29=-6
log%285%2C%28x%2Fx%5E3%29%29=-6
5^-6=1/x^2
x^2=1/5^-6
x=±1/5^-3
x=125
check:
log(base 125)x=log(base 125)(125)=1
log(base 5)x=log(base 5)(125)=3
log(base 125)x - log(base 5)x=1-3=-2