SOLUTION: If log(base 5)2 = m , express log 20 in terms of m. I tried splitting log 20 into log 2 + log 10 = log 2 + 1 And played around with log(base 5)2 = log2/log5 = m But I can't re

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: If log(base 5)2 = m , express log 20 in terms of m. I tried splitting log 20 into log 2 + log 10 = log 2 + 1 And played around with log(base 5)2 = log2/log5 = m But I can't re      Log On


   

Question 629058: If log(base 5)2 = m , express log 20 in terms of m.
I tried splitting log 20 into log 2 + log 10 = log 2 + 1
And played around with log(base 5)2 = log2/log5 = m
But I can't reach the answer of (2m+1)/(m+1)
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If log(base 5)2 = m , express log 20 in terms of m.
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log%285%2C2%29+=+m
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If you mean log%2810%2C20%29
then,
log%285%2C2%29+=+m
20 = 2*5*2
log(20) = log(2) + log(5) + log(2) to any base
log%285%2C20%29+=+m+%2B+1+%2B+m+=+2m%2B1
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log%285%2C10%29+=+log%282%29+%2B+log%285%29+=+m%2B1
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Use base change:
log%2810%2C20%29+=+log%285%2C20%29%2Flog%285%2C10%29
= (2m+1)/(m+1)