SOLUTION: I'm having issues with logarithms. I'm studying for my final and this is the first question on my review: log(subset x)(8/125)=3 I began by applying the quotient rule and came

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Question 80153: I'm having issues with logarithms. I'm studying for my final and this is the first question on my review:
log(subset x)(8/125)=3
I began by applying the quotient rule and came up with:
log(subset x)8-log(subset)125=3
I thought I would rewrite it as log(subset x)(8x125)=3, but I have no clue.
I believe I would know what to do if there weren't constants in the equation, but I cannot figure this out.
My answer options are:
a) 2/5
b) 5/2
c) 3
d) 8
Thank you so much!
Answer by tutor_paul(427) (Show Source):
You can put this solution on YOUR website!
You need to recognize the key fact that a logarithm is an exponent. So the equation log(base x)(8/125)=3 can be re-written as follows:

Now you just take the cube root of each side to solve for x. You will find that

Good Luck,
tutor_paul@yahoo.com