A-Level CAIE Mathematics AS 2.2 Logarithmic and exponential functions Question Bank

Sketch the graph of $y=\mathrm{e}^{a x}-1$ where a is a positive constant.

Use logarithms to solve the equation $5^{3 x-1}=2^{4 x}$, giving your answer correct to 3 significant figures.

Solve the equation $\ln \left(x^{2}+4\right)=2 \ln x+\ln 4$, giving your answer in an exact form.

Given that $5^{x}=3^{4 y}$, use logarithms to show that y=m x and find the value of the constant m correct to 3 significant figures.

Use logarithms to solve the equation

giving the answer correct to 3 significant figures.

Solve the equation $2 \ln (2 x)-\ln (x+3)=\ln (3 x+5)$.

Solve the equation $\left|2^{x}-7\right|=1$, giving answers correct to 2 decimal places where appropriate.

It is given that $z=\ln (y+2)-\ln (y+1)$. Express y in terms of z.

Solve the equation $\ln (3 x+1)-\ln (x+2)=1$, giving your answer in terms of e.