Mathematics 9709 · AS & A Level · Logarithmic and exponential functions
Logarithmic and exponential functions — practice question
The variables $x$ and $y$ satisfy the relation $2^y = 3^{1-2x}$.
(a)[3]
By taking logarithms, show that the graph of $y$ against $x$ is a straight line. State the exact value of the gradient of this line.
(b)[2]
Determine the exact $x$-coordinate of the point where this line intersects $y = 3x$. Present your answer in the form $\frac{\ln a}{\ln b}$, with $a$ and $b$ integers.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State or indicate $\log y=2\log 3-2x\log 3$” …