Hi,

My elderly father has been stumped by the following questions for the past few days. It's beyond my knowledge. I wondered if anyone here might be able to solve these two attached questions 10 and 16 (I did try to write them out and use LATEX code but to no avail)?

Many thanks in advance.

Here's my efforts using LATEX

Q10: Show that log_{16} $\displaystyle (xy)$= $\displaystyle \frac{1}{2}$ $\displaystyle log_4$ $\displaystyle x$+$\displaystyle \frac{1}{2}$ $\displaystyle log_4$ $\displaystyle y$. Hence, or otherwise, solve the simutaneous equations

log_16 $\displaystyle (xy)$=3 $\displaystyle \frac{1}{2}$

(($\displaystyle log_4$ $\displaystyle x$) / ($\displaystyle log_4$ $\displaystyle y$)) = -8

Q16: Express log_9 $\displaystyle x$$\displaystyle y$ in terms of $\displaystyle log_3$ $\displaystyle x$ and $\displaystyle log_3$ $\displaystyle y$.

Without using tables, solve for x and y the simultaneous equations

log_9 $\displaystyle x$ $\displaystyle y$= $\displaystyle \frac{5}{2}$

$\displaystyle log_3$ $\displaystyle x$ $\displaystyle log_3$ $\displaystyle y$ = -6