CAIE A-Level Mathematics 2.2.3 Log equations

Practise solving equations and inequalities where the unknown is in an index, using logarithms and substitutions such as e^x.

Exam points

take logs of both sides and apply the power law to make x appear outside indices
solve quadratic forms in e^x or e^{2x}, rejecting impossible negative exponential values

[Maximum number: 2]

Hence solve the equation $\mathrm{e}^{-12 y}-32 \mathrm{e}^{-3 y}+48=0$ , giving your answer in an exact form.

Apply logarithms and use power law for $\mathrm{e}^{-3 y}=k$ where k>0
M1
Obtain $y=-\frac{1}{3} \ln 2, \frac{1}{3} \ln \frac{1}{2}$
A1
Or exact equivalent
Must be simplified e.g. not lne or $\frac{6}{3}$
ISW extra solutions but A0 if undefined solutions are included.

All question bank results loaded

2.2.3—Log equations question 1