# Math Help - logarithm conversion

1. ## 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 $\frac {1}{2}*2x^2$

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

3. 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?

4. 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:

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

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

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