Show that $\log_{9}{(\cos{2x} + 2)} = \log_{3}{\sqrt{\cos{2x} + 2}}$. [3] Hence or otherwise solve

Question

Show that $\log_{9}{(\cos{2x} + 2)} = \log_{3}{\sqrt{\cos{2x} + 2}}$. [3] Hence or otherwise solve $\log_{3}{(2\sin{x})} = \log_{9}{(\cos{2x} + 2)}$ for $0 < x < \frac{\pi}{2}$. [5]

Accepted Answer

(b) $x = \frac{\pi}{4}$

Specimen Paper SPEC/5/TZ0 P1 Q6

Specimen Paper SPEC/5/TZ0 P1 Q6