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

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> 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      Log On


   

Question 655680: I get different answers depending on how I simplify the expression 5%5E%283log%2825%2Ca%29%29. This shows me that I must be awfully confused about log rules. WolframAlpha gives a%5E%283%2F2%29, which I figured out can be done thusly:

5%5E%283log%2825%2Ca%29%29=x
3log%2825%2Ca%29=log%285%2Cx%29
3log%285%2Ca%29%2Flog%285%2C25%29=log%285%2Cx%29
%283%2F2%29%2Alog%285%2Ca%29=log%285%2Cx%29%29
log%285%2C%28a%5E%283%2F2%29%29%29=log%285%2Cx%29
a%5E%283%2F2%29=x

If I do it another way, I get my answer as a%5E3-25. Here is how I did that:

But if I do it another way, I get the answer as 5^(2/3)+a. See:
5%5E%283log%2825%2Ca%29%29=x
3log%2825%2Ca%29=log%285%2Cx%29
3=log%285%2Cx%29%2Flog%2825%2Ca%29
3=log%285%2Cx%29%2F%28log%285%2Ca%29%2Flog%285%2C25%29%29
3=log%285%2Cx%29%2Flog%285%2C%28a-25%29%29
3=log%285%2C%28x-a%2B25%29%29
5%5E3=x-a%2B25
5%5E3-25%2Ba=x
100%2Ba=x
And even a third answer:
5%5E%283log%2825%2Ca%29%29=x
3log%2825%2Ca%29=log%285%2Cx%29
3log%285%2Ca%29%2Flog%285%2C25%29=log%285%2Cx%29
%283%2F2%29%2Alog%285%2Ca%29=log%285%2Cx%29%29
3%2F2=log%285%2Cx%29%2Flog%285%2Ca%29
3%2F2=log%285%2C%28x-a%29%29
5%5E%283%2F2%29=x-a
5%5E%283%2F2%29%2Ba=x
Found 3 solutions by Alan3354, moyshekapoyre, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I get different answers depending on how I simplify the expression 5%5E%283log%2825%2Ca%29%29
===========================
5%5E%283log%2825%2Ca%29%29
= 5%5E%28log%2825%2Ca%5E3%29%29
Since 25 = 5^2:
= 5%5E%28log%285%2Ca%5E6%29%29
= a%5E6

Answer by moyshekapoyre(1) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
I did it and also got: a%5E%283%2F2%29. Therefore: 5%5E%283log%2825%2Ca%29%29 = a%5E%283%2F2%29

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

5%5E%283log%2825%2Ca%29%29 ------ 5%5E%28log%2825%2Ca%5E3%29%29

Substituting 25 for a in 5%5E%28log%2825%2Ca%5E3%29%29 results in: 5%5E%28log%2825%2C25%5E3%29%29

Since log%2825%2C25%5E3%29 = 3, then 5%5E%28log%2825%2C25%5E3%29%29 = 5%5E3, or highlight%28125%29

Now, substituting 25 for a into the simplified version/answer of a%5E%283%2F2%29 gives us: 25%5E%283%2F2%29 ----- %28sqrt%2825%29%29%5E3 ------ 5%5E3, or highlight%28125%29.

This clearly proves that your 1st answer that 5%5E%283log%2825%2Ca%29%29 simplifies to highlight_green%28a%5E%283%2F2%29%29 is unequivocally 100% correct.

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