One More Single Log

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August 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."
August 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."

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

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

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

$= \, ....$
August 7th 2008, 07:32 PM
magentarita

Then...

Is the last expression the answer?
August 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 $\log A - \log B = \log \frac{A}{B}$ to get an expression in the form of a single logarithm ....
August 8th 2008, 06:49 AM
magentarita

ok...

That's what I thought.

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