# One More Single Log

• Aug 7th 2008, 02:45 AM
magentarita
One More Single Log
Write the expression below as a single logarithm.

3 log_5 (3x + 1) - 2 log_5(2x - 1) - log_5 (x)

NOTE: log_5 means "log base 5."
• Aug 7th 2008, 03:26 AM
mr fantastic
Quote:

Originally Posted by magentarita
Write the expression below as a single logarithm.

3 log_5 (3x + 1) - 2 log_5(2x - 1) - log_5 (x)

NOTE: log_5 means "log base 5."

$\displaystyle = \log_5 (3x + 1)^3 - \log_5 (2x - 1)^2 - \log_5 (x)$

$\displaystyle = \log_5 (3x + 1)^3 - \left[ \log_5 (2x - 1)^2 + \log_5 (x) \right]$

$\displaystyle = \log_5 (3x + 1)^3 - \log_5 \left( (2x-1)^2 x \right)$

$\displaystyle = \, ....$
• Aug 7th 2008, 07:32 PM
magentarita
Then...
Is the last expression the answer?
• Aug 7th 2008, 08:38 PM
mr fantastic
Quote:

Originally Posted by magentarita
Is the last expression the answer?

Is the last expression in the form of a single logarithm?

Now you have to use the log rule $\displaystyle \log A - \log B = \log \frac{A}{B}$ to get an expression in the form of a single logarithm ....
• Aug 8th 2008, 06:49 AM
magentarita
ok...
That's what I thought.