# Solving Log

• Oct 21st 2011, 03:28 PM
brian890
Solving Log
Given that log2=r, and log3=s, express the following in terms of r and s.
log18 and log15

I think I did the first one right, but I'm not sure
=log(3x3x2)
=log3+log3+log2
=s+s+r
=2s+r

But I'm not sure how to do the second one.
• Oct 21st 2011, 05:19 PM
Soroban
Re: Solving Log
Helo, brian890!

Quote:

Given that: .$\displaystyle \log2=r\,\text{ and }\,\log3=s$,
express the following in terms of $\displaystyle r$ and $\displaystyle s$.

$\displaystyle (a)\;\log(18)$

I think I did the first one right, but I'm not sure

$\displaystyle \log(18) \:=\:\log(3\!\times\!3\!\times\!2) \:=\:\log3\!+\!\log3\!+\!\log2 \;=\;s\!+\!s\!+\!r \;=\;2s+r$
Right!

Quote:

$\displaystyle (b)\;\log(15)$

I assume these logs are base-ten.

We have: .$\displaystyle \log_{10}(15) \:=\:\log_{10}\left(\frac{3\cdot10}{2}\right)$

. . . . . . . . . . . . . . . $\displaystyle =\:\log_{10}(3) + \log_{10}(10) - \log_{10}(2)$

. . . . . . . . . . . . . . . $\displaystyle =\; s + 1 - r$