# Solution to #1-9

Paper 1 Difficulty: Medium

Let $log_{8}A=x, \, log_{8}B=y, \, log_{8}C=z$. Express $log_{8}\left ( \frac{A^{2}}{B^{3}C} \right )^{4}$ in terms of x, y and z.

[Maximum mark: 3]

$log_{8}\left ( \frac{A^{2}}{B^{3}C} \right )^{4} = 4 log_{8}\left ( \frac{A^{2}}{B^{3}C} \right ) = 4 \left (log_{8}A^{2} – log_{8}B^{3}C \right ) = 4 \left ( 2log_{8}A – 3log_{8}B – log_{8}C \right) =$

$= 4 \left (2x – 3y – z \right ) = 8x – 12y – 4z$.