Logarithmic Expression

**Pernello** · July 26th 2012, 04:06 AM

How would this be simplified?

I understand what would be done if the base on the logarithm were 9 but what happens in a case like this?
Any help would be greatly appreciated.

**emakarov** · July 26th 2012, 04:23 AM

Use the fact that $(x^a)^b=(x^b)^a=x^{ab}$ .

**Prove It** · July 26th 2012, 04:24 AM

Originally Posted by Pernello

How would this be simplified?

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I understand what would be done if the base on the logarithm were 9 but what happens in a case like this?
Any help would be greatly appreciated.

$\displaystyle \begin{align*} 9^{\log_3{20}} &= \left(3^2\right)^{\log_3{20}} \\ &= 3^{2\log_3{20}} \\ &= 3^{\log_3{\left(20^2\right)}} \\ &= 20^2 \\ &= 400 \end{align*}$

**Neeraj** · July 26th 2012, 04:31 AM

see formula in image, so that u can clear what is the answer
9 log3 20 = 20 log3 9
= 20 log3 (32)
= 20 2 log 33
= 20 2 *1
=20 2 = 400

**Wilmer** · July 26th 2012, 04:38 AM

x = log(3)20 = log(20) / log(3) ; 9^x = ?

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