Logarithmic and Exponential Functions Past Paper Questions — 9709 Paper 3

Q12025 Feb/Mar·P323MMedium-EasyLogarithmic and Exponential Functions

Solve the equation

\ln(1 - e^{-2x}) + 3 = 0

Give your final answer correct to 4 decimal places.

Q22025 May/Jun·P313MMedium-EasyLogarithmic and Exponential Functions

It is given that $2\ln p + \ln(p - 1) - \frac{1}{2}\ln(q + 1) = 3$ .

Find $q$ in terms of $p$ .

Q12025 May/Jun·P325MMediumLogarithmic and Exponential Functions

Solve the equation

\frac{e^x + 2e^{-x}}{e^x - 3} = 4

Give your answer correct to 3 decimal places.

Q22025 May/Jun·P334MMediumLogarithmic and Exponential Functions

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

Q12025 May/Jun·P354MMedium-EasyLogarithmic and Exponential Functions

Solve the equation $3^{4-2x} = 5(6^{x-1})$ . Give your answer correct to 3 significant figures.

Q22025 Oct/Nov·P312 partsMediumLogarithmic and Exponential Functions

(a)

Show that the equation $\log_4(2x + 1) = 2\log_4(3x - 1) - 2$ can be written as a quadratic equation in $x$ .

(b)

Hence solve the equation $\log_4(2x + 1) = 2\log_4(3x - 1) - 2$ .

Q22025 Oct/Nov·P324MMediumLogarithmic and Exponential Functions

Solve the equation $3 \times 2^{x+1} = 4 \times 3^{2x-3}$ . Give your answer correct to 3 significant figures.

Q32025 Oct/Nov·P334MMedium-EasyLogarithmic and Exponential Functions

Solve the equation $2^{3x-4} = \frac{3}{5^x}$ . Give your answer in the form $\frac{\ln m}{\ln n}$ , where $m$ and $n$ are integers.

Q32025 Oct/Nov·P352 partsMedium-EasyLogarithmic and Exponential Functions

(a)

Show that the graph of $\ln y$ against $x$ is a straight line.

(b)

When $x = 3.4$ , $\ln y = 0.86$ and when $x = 5.7$ , $\ln y = 2.56$ .

Find the value of $A$ and the value of $b$ . Give your answers correct to 2 significant figures.

Q42024 Feb/Mar·P324MMediumLogarithmic and Exponential Functions

The positive numbers $p$ and $q$ are such that

\ln\left(\frac{p}{q}\right) = a \quad \text{and} \quad \ln(q^2p) = b.

Express $\ln(p^7q)$ in terms of $a$ and $b$ .