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.
Helo, brian890!
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!
$\displaystyle (b)\;\log(15)$
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) $
. . . . . . . . . . . . . . . $\displaystyle =\; s + 1 - r$