Solve ${{\log }_{3}}x-6{{\log }_{x}}3=1$. [4] The curve $y=\ln \left( 2x+{{e}^{2}} \right)$ cuts the

Question

Solve ${{\log }_{3}}x-6{{\log }_{x}}3=1$. [4] The curve $y=\ln \left( 2x+{{e}^{2}} \right)$ cuts the coordinates axes at $\left( 0,h \right)$ and $\left( k,0 \right)$. The curve $y=\frac{1}{2}-{{e}^{ax}}$ passes through the point $\left( h,k \right)$. Find the exact values of $h$, $k$ and $a$. [4]

Accepted Answer

(a) $x = \frac{1}{9}$ \text{ or } $x = 27$ (b) $a = 1 + \frac{1}{2}\ln\frac{1}{2}$

2020 HGSS AM S4 P2 Q9

2020 HGSS AM S4 P2 Q9

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