SOLUTION: 25^x-1=125^4x

Question 288641: 25^x-1=125^4x
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

The simplest solution to this is based on recognizing that both 25 and 125 are powers of 5. So we can express both side as powers of 5:

Using the proper rule for exponents (i.e. multiply them) we get:

With both sides now being powers of 5, they can only be equal if the exponents are the same:
2x-2 = 12x
Solving this:
-2 = 10x
-2/10 = x
-1/5 = x

If you don't recognize that 25 and 125 are powers of 5 we can still use logarithms:

We can use our calculators on this. We should get -0.2 (or some decimal very close to it). 0.2 is the decimal for 1/5 so the answer is still the same as before.
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