- #1

gl0ck

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## Homework Statement

Hi, it maybe stupid question, but I struggle on this problem..

log

_{16}(4

^{3}5

^{4})+3/log

_{25}(4

^{3})=a+b*log

_{2}5

## Homework Equations

Using properties:

log

_{a}b

^{n}=n log

_{a}b

log

_{n}(bc) = log

_{n}b+log

_{n}c

log

_{b}a=1/log

_{a}b

## The Attempt at a Solution

I can't find the b number.

log

_{16}(4

^{3}5

^{4})+3/log

_{25}(4

^{3})=6 log

_{16}2+4log

_{16}5+3/3log

_{25}4=6(log

_{2}2/log

_{2}16)+4(log

_{2}5/log

_{2}16)+1/log

_{25}4=3/2 + 2log

_{2}5

^{2}= 3/2 + 4log

_{2}5

so a=3/2 b=4 but in the answer they find b to be 2 not 4

Can you please tell me where is my mistake?

Thanks

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