Mathematics (Factoring and Logarithms)

I have a question. My book does not cover this, and I have been unable to locate anything on this online. Can you Factor inputs out of a logarithm?

Is the following valid? Please forgive the elementary question, but I feel it is important to get a good grasp on math to fine tune my code.

Code:

`ln(2x)=ln(3x)`

ln(2) + ln(x) = ln(3) + ln(x)

ln(x) - ln(x) = ln(3) - ln(2)

x ( ln() - ln() ) = ln (3/2)

x = ln (3/2)

if this is valid, what other properties/laws can I apply to logarithms?

associative, distributive, etc.

is there a list of these?

I found this site, but no answer to these questions.

http://mathworld.wolfram.com/Logarithm.html