# logarithm conversion

• July 23rd 2009, 07:09 PM
chengbin
logarithm conversion
I want to rewrite $\ln x$ to (something) $\ln 3x$.

Is that possible?

For example, if I want to rewrite $x^2$ to (something) $2x^2$, it becomes $\frac {1}{2}*2x^2$
• July 23rd 2009, 07:14 PM
pickslides
$ln(x) = - ln(3)+ ln(3x)$
• July 23rd 2009, 07:17 PM
chengbin
Quote:

Originally Posted by pickslides
$ln(x) = - ln(3)+ ln(3x)$

Do you mind showing the logic behind this conversion? Thank you.

Also, is it possible to rewrite it with only 1 term instead of 2?
• July 23rd 2009, 07:24 PM
pickslides
I don't know if it can be done with 1 term.

The logic behind my post is simply the addition of logs law, it is:

$ln(a) + ln(b) = ln(a\times b)$

$ln(b) = - ln(a) + ln(a\times b)$

$ln(x) + ln(3) = ln(3x)$
$ln(x) = - ln(3)+ ln(3x)$