Paper 1 · Exponentials and logarithms

Solve the equation $e^{2x} = 4e^{2-x}$ , giving your answer in exact form.

x = 2 + \ln 4

x = \tfrac{1}{3}\ln 4 - 2

x = \tfrac{1}{3}(2 + \ln 4)

x = \tfrac{1}{2}(2 + \ln 4)

Explanation: Dividing gives

e^{2x-(2-x)}=e^{3x-2}=4

, so

3x-2=\ln4

and

x=\tfrac13(2+\ln4)

Derived from ZIMSEC Mathematics Paper 1, June 2018, Q1

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