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

Logarithmic and exponential functions — practice question

The variables $x$ and $y$ are linked by $3^y = 4^{2 - x}$.

(a(i))[3]

Using logarithms, demonstrate that the graph of $y$ plotted against $x$ is a straight line. Give the exact gradient of the line.

(a(ii))[2]

Calculate the exact $x$-coordinate of the point where this line intersects the line $y = 2x$, and simplify your answer.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State or imply that $y\ln 3 = (2-x)\ln 4$.” …