Mathematics 9709 · AS & A Level · Logarithmic and exponential functions

Logarithmic and exponential functions — practice question

The variables $x$ and $y$ obey the equation $x^n y^2 = C$, where $n$ and $C$ are constants. The straight-line graph of $\ln y$ against $\ln x$ goes through the points $(0.31, 1.21)$ and $(1.06, 0.91)$, as illustrated in the diagram.
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Determine the value of $n$ and determine the value of $C$ correct to 2 decimal places.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: State or show that $n\ln x+2\ln y=\ln C$.

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