1.express in terms of log a, log b.
$\displaystyle \log \frac{1}{ab^4}$
2.express as a single logarithm.
$\displaystyle \frac{1}{2}\log 80 - \frac{1}{2}\log 5$
thanks
for 1 i had trouble of how to manipulate the fraction $\displaystyle \frac{1}{ab^4}$.
is this the correct form? $\displaystyle \log a - \log b ^ -4$
for 2 i did using the laws of logs.
$\displaystyle \log 80^\frac{1}{2} - \log 5^\frac{1}{2}$
then $\displaystyle \log \frac{\log \sqrt{80}}{\log \sqrt{5}}$
Using the properties posted above by Defunkt, you get:
$\displaystyle log\left ( \frac{1}{ab^4}\right )$
$\displaystyle \Rightarrow log(1)-\left[log(a)+log(b^4)\right]$
$\displaystyle \Rightarrow 0-log(a)-4log(b)$
$\displaystyle \Rightarrow -log(a)-4log(b)$
and for the second one:
$\displaystyle \frac{1}{2}log(80)-\frac{1}{2}log(5)$
$\displaystyle \Rightarrow \frac{1}{2}\left[log(80)-log(5)\right]$
$\displaystyle \Rightarrow\frac{1}{2}log(\frac{80}{5})$
$\displaystyle \Rightarrow\frac{1}{2}log(16)$
$\displaystyle \Rightarrow\log(16^\frac{1}{2})$
$\displaystyle \Rightarrow\log(4)$