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

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_23 Year：2021 Question No：5(c)

Answer:

Apply logarithms and use power law for $\mathrm{e}^{-3 y}=k$ where $k>0$
Obtain $y=-\frac{1}{3} \ln 2, \frac{1}{3} \ln \frac{1}{2}$

2.2.3 use logarithms to solve equations and inequalities in which the unknown appears in indices