# How do I write this as a single logarithm?

• Jan 29th 2008, 03:35 PM
Jeavus
How do I write this as a single logarithm?
http://img167.imageshack.us/img167/8...nglelogjg9.png

This is what the question reads.

"Write the following as a single logarithm."

(4log5x - 2log5y)/ 3log5w
= (log5x^4 / log5y^2) / log5w^3

Is that it?

Or...

(4log5x - 2log5y)/ 3log5w
= (log5x^4 / log5y^2) - log5w^3

I'm a bit confused with this specific problem.
• Jan 29th 2008, 04:04 PM
TrevorP
First take the powers leading co-efficients from in front of the logs to get:

$\frac{\log_5 x^4 - \log_5 y^2}{\log_5 w^5}$

Then join the subtraction to get:

$\frac{\log_5 \frac{x^4}{y^2}}{\log_5 w^5}$

Now since they have a common base you can do this:

$\log_{w^5}{\tfrac{x^4}{y^2}}$