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

Use logarithms to solve the equation

giving the answer correct to 3 significant figures.

It is given that $x=\ln (2 y-3)-\ln (y+4)$.
Express y in terms of x.

Solve the equation $2^{3 x-1}=5\left(3^{1-x}\right)$. Give your answer in the form $\frac{\ln a}{\ln b}$ where a and b are integers.

Solve the equation $2\left(3^{2 x-1}\right)=4^{x+1}$, giving your answer correct to 2 decimal places.

Find the value of x for which $3\left(2^{1-x}\right)=7^{x}$. Give your answer in the form $\frac{\ln a}{\ln b}$, where a and b are integers.

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

Solve the equation $5 \ln \left(4-3^{x}\right)=6$. Show all necessary working and give the answer correct to 3 decimal places.

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

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

Given that $5^{3 x}=7^{4 y}$, use logarithms to find the value of $\frac{x}{y}$ correct to 4 significant figures.