Given that ${{\log }_{\sqrt{2}}}x=m$ and ${{\log }_{4}}y=n$, express $\frac{\sqrt{y}}{{{x}^{6}}}$ in

Question

Given that ${{\log }_{\sqrt{2}}}x=m$ and ${{\log }_{4}}y=n$, express $\frac{\sqrt{y}}{{{x}^{6}}}$ in terms of $m$ and $n$. [4] Solve the equation ${{\log }_{2}}\left( 3x-2 \right)={{\log }_{4}}\left( {{x}^{2}}+1 \right)+\frac{2}{{{\log }_{\sqrt{2}}}2}$. [6]

Accepted Answer

(a) $2^{n-3m}$. (b) $x=12/5$.

2020 ANDSS AM S4 P2 Q4

2020 ANDSS AM S4 P2 Q4

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