Logarithmic and Exponential Functions Past Paper Questions — 9709 Paper 2

Q12025 Feb/Mar·P223MMedium-EasyLogarithmic and Exponential Functions

Solve the equation $\ln(3x + 1) - \ln(x - 5) = \ln 7$ .

Q12025 May/Jun·P253MMedium-EasyIntegration

Show that

\int_2^{11} \frac{8}{4x+1}\,dx = \ln a

where $a$ is an integer to be found.

Q22025 Oct/Nov·P213MMedium-EasyLogarithmic and Exponential Functions

Solve the equation $e^{2x}(e^{2x} - 8) = 48$ .

Q52025 Oct/Nov·P212 partsMedium-EasyLogarithmic and Exponential Functions

(a)

Show that the $x$ -coordinate of $B$ is $6\ln 2$ .

(b)

Find the area of the shaded region. Give your answer in the form $p\ln 2 - q$ , where $p$ and $q$ are positive integers.

Q12025 Oct/Nov·P224MMedium-EasyLogarithmic and Exponential Functions

Solve the equation $\ln(3x + 5) - \ln(x - 2) = 4$ . Give your answer in an exact form.

Q22025 Oct/Nov·P233MMedium-EasyLogarithmic and Exponential Functions

Solve the equation $e^{2x}(e^{2x} - 8) = 48$ .

Q22025 Oct/Nov·P253MMedium-EasyLogarithmic and Exponential Functions

Solve the equation $e^{2x}(e^{2x} - 8) = 48$ .

Q12024 Feb/Mar·P224MMedium-EasyLogarithmic and Exponential Functions

Use logarithms to solve the equation $3^{4x+3} = 5^{2x+7}$ . Give your answer correct to 3 significant figures.

Q22024 May/Jun·P224MMedium-EasyLogarithmic and Exponential Functions

Use logarithms to solve the equation $6^{2x-1} = 5e^{3x+2}$ . Give your answer correct to 4 significant figures.

Q22024 May/Jun·P234MMedium-EasyLogarithmic and Exponential Functions

Use logarithms to solve the equation $6^{2x-1} = 5e^{3x+2}$ . Give your answer correct to 4 significant figures.