1. ## Logs help

Given that $p=\log_{q}16$, express $\log_{q}2$ and $\log_{2}8q$ in terms of p.

The answers are $\frac{p}{4}$ and $3+\frac{4}{p}$ respectively. I kind of get why the first one would be that but I really don't know how to work either of them out

2. Originally Posted by greghunter
Given that $p=\log_{q}16$, express $\log_{q}2$ and $\log_{2}8q$ in terms of p.

The answers are $\frac{p}{4}$ and $3+\frac{4}{p}$ respectively. I kind of get why the first one would be that but I really don't know how to work either of them out
$\log_q2^4=p$

$4\log_q2=p$

$\log_q2=\frac{p}{4}$

For no. 2)

Write $\log_28q$ as $\log_2(8\cdot q)=\log_28+\log_2q$

$\log_28q=3+\frac{1}{\log_q2}$

$\log_28q=3+\frac{4}{p}$