# Logarithms: Evalute or simplify

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• Jul 28th 2010, 04:06 PM
danielh9103
Logarithms: Evalute or simplify
Evaluate or simplify

5^(3log57)
• Jul 28th 2010, 04:11 PM
pickslides
Use 2 log laws.

$a\log_bc = \log_bc^a$

then

$a^{\log_ab^c} = b^c$
• Jul 28th 2010, 04:13 PM
Archie Meade
Quote:

Originally Posted by danielh9103
Evaluate or simplify

5^(3log57)

Simplifying..

$5^y=x\ \Rightarrow\ y=log_5x$

$3log_57=log_5x$

$log_5\left(7^3\right)=log_5x$
• Jul 28th 2010, 04:25 PM
habibixox
@Archie Meade

i feel it can be simplified more... or is that the final answer?

obviously you can simplify 7^3 or would that be incorrect?
• Jul 28th 2010, 04:35 PM
Archie Meade
Quote:

Originally Posted by habibixox
@Archie Meade

i feel it can be simplified more... or is that the final answer?

obviously you can simplify 7^3 or would that be incorrect?

Yes, habibixox,

just evaluating that power gives the very final value of x, the last calculation required,
but that preceding piece is all that is required to say goodbye to the logarithm part.