Given that $p={{3}^{x}}$ and $q={{3}^{y}}$, express ${{\log }_{3}}\frac{{{p}^{7}}q}{243}$ in t

Question

Given that $p={{3}^{x}}$ and $q={{3}^{y}}$, express ${{\log }_{3}}\frac{{{p}^{7}}q}{243}$ in terms of $x$ and $y$. [4] Given that ${{\log }_{2}}x-{{\log }_{x}}{{x}^{2}}=\frac{1}{3}-{{\log }_{8}}2x$, find the value of $x$, leaving your answer in index form.[4]

Accepted Answer

(a) $7x+y-5$. (b) $x=2\sqrt2$.

2020 AHS AM S4 P2 Q3

2020 AHS AM S4 P2 Q3

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