SOLUTION: I get different answers depending on how I simplify the expression {{{5^(3log(25,a))}}}. This shows me that I must be awfully confused about log rules. WolframAlpha gives {{{a^(3/2

Question 655680: I get different answers depending on how I simplify the expression . This shows me that I must be awfully confused about log rules. WolframAlpha gives , which I figured out can be done thusly:

If I do it another way, I get my answer as . Here is how I did that:

But if I do it another way, I get the answer as 5^(2/3)+a. See:

And even a third answer:

Found 3 solutions by Alan3354, moyshekapoyre, MathTherapy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
I get different answers depending on how I simplify the expression
===========================

=
Since 25 = 5^2:
=
=

Answer by moyshekapoyre(1)   (Show Source): You can put this solution on YOUR website!
Alan, that is illegal. Replace a with 25 and you will see it makes no sense.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
I did it and also got: . Therefore: =

This is the correct answer and can be proven as follows:

------

Substituting for a in results in:

Since = 3, then = , or

Now, substituting for a into the simplified version/answer of gives us: ----- ------ , or .

This clearly proves that your 1st answer that simplifies to is unequivocally 100% correct.

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