# Logarithmic Expression

• Jul 26th 2012, 04:06 AM
Pernello
Logarithmic Expression
How would this be simplified?

Attachment 24350

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.
• Jul 26th 2012, 04:23 AM
emakarov
Re: Logarithmic Expression
Use the fact that $(x^a)^b=(x^b)^a=x^{ab}$.
• Jul 26th 2012, 04:24 AM
Prove It
Re: Logarithmic Expression
Quote:

Originally Posted by Pernello
How would this be simplified?

Attachment 24350

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*}
• Jul 26th 2012, 04:31 AM
Neeraj
Re: Logarithmic Expression
Attachment 24354

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
• Jul 26th 2012, 04:38 AM
Wilmer
Re: Logarithmic Expression
x = log(3)20 = log(20) / log(3) ; 9^x = ?