# simplify number raised to a logarithm exponent

• Aug 16th 2008, 04:28 PM
apm
simplify number raised to a logarithm exponent
3^log325

thank you
• Aug 16th 2008, 04:42 PM
mr fantastic
Quote:

Originally Posted by apm
3^log325

thank you

Let $a^{\log_{a} b} = c$. Take log to base a of both sides:

$\log_{a} b = \log_{a} c$.

What do you conclude? So the answer to your question is ......
• Aug 16th 2008, 04:42 PM
Chop Suey
$3^{\log_3{25}} = 25$

Because $3$ and $\log_3$ are inverse operations:

$3^{\log_3{x}} = x$

$\log_3{3} = 1$

$3^1 = 3 \implies 3^{\log_3{3}} = 3$

EDIT: Mr. F, you're too fast. :p
• Aug 16th 2008, 04:56 PM
apm
thanks!