# Some number to an exponent of a log

I need to simplify an expression. I am currently working on the following problem (I apologize in advance for formatting, I'm not sure how to use it on Stack Exchange):

$81^{(\log_{3}N)+(log_{9}N)}$

It's been several years since I've taken algebra so I do not remember at all how to simplify this. I'm not asking for or need an exact answer, but some guidance on how to do it on my own would be entirely beneficial to doing problems like this in the future.

• Directions for use of LateX to properly write mathematics in this site can be found in the FAQ section. – DonAntonio Apr 10 '13 at 2:14
• Oh I'm familiar with Latex. Didn't know the site used it. Sorry about that. – Ampage Grietu Apr 10 '13 at 2:21

$$81^{\log_3N+\log_9N}=3^{4\log_3N+4\log_9N}=3^{\log_3N^4}\cdot9^{\frac{1}{2}\log_9N^4}=N^4N^2\ldots$$