Logarithms: Evalute or simplify

**danielh9103** · July 28th 2010, 04:06 PM

Evaluate or simplify

5^(3log57)

**pickslides** · July 28th 2010, 04:11 PM

Use 2 log laws.

$a\log_bc = \log_bc^a$

then

$a^{\log_ab^c} = b^c$

**Archie Meade** · July 28th 2010, 04:13 PM

Originally Posted by danielh9103

Evaluate or simplify

5^(3log57)

Simplifying..

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

$3log_57=log_5x$

$log_5\left(7^3\right)=log_5x$

**habibixox** · July 28th 2010, 04:25 PM

@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?

**Archie Meade** · July 28th 2010, 04:35 PM

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.

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