# Logarithms

• Oct 12th 2010, 07:29 AM
rtblue
Logarithms
Hello everyone, I had a question about a problem involving some logs:

$\displaystyle 5log_32+2log_910=?$

I'm not quite sure where to start with this problem, any suggestions would be appreciated.
• Oct 12th 2010, 07:36 AM
TheEmptySet
Quote:

Originally Posted by rtblue
Hello everyone, I had a question about a problem involving some logs:

$\displaystyle 5log_32+2log_910=?$

I'm not quite sure where to start with this problem, any suggestions would be appreciated.

A good place to start might be to use the change of base formula
Logarithm - Wikipedia, the free encyclopedia

$\displaystyle \log_9(a)=\frac{\log_{3}(a)}{\log_3(9)}=...$

You will need to use other log properties as well.
• Oct 12th 2010, 07:38 AM
Plato
Hint: $\displaystyle 2\log_9(10)=\log_3(10)$.
• Oct 12th 2010, 11:34 AM
HallsofIvy
That's because $\displaystyle y= log_9(x)$ is the same as $\displaystyle x= 9^y= (3^2)^y= 3^{2y}$ so that $\displaystyle log_3(x)= 2y= 2log_9(x)$.
• Oct 12th 2010, 12:21 PM
bigwave
use ln
using as has been mentioned you could too rewrite to:

$\displaystyle \log_3{32} + \log_9{100}$

then

$\displaystyle \frac{ln32}{ln3} + \frac{ln100}{ln9} \Rightarrow 3.15 + 4.19 = 5.25$(approx)