logarithm conversion

**chengbin** · July 23rd 2009, 07:09 PM

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

**pickslides** · July 23rd 2009, 07:14 PM

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

**chengbin** · July 23rd 2009, 07:17 PM

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?

**pickslides** · July 23rd 2009, 07:24 PM

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:

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

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

In your case

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

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

**chengbin** · July 23rd 2009, 07:27 PM

Looks like I was late.

I got how the conversion works on my bed, I got up to tell you I got it and don't bother explaining it. Thanks anyways.

**pickslides** · July 23rd 2009, 07:33 PM

Not to worry. Good luck!

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