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0606 P22 - Jun 2020 - Q9 - 8 marks
8148

(a) Solve the equation

\(\frac{9^{5x}}{27^{x-2}}=243.\)

(b) Given that

\(\log_a\sqrt b-\frac12=\log_b a,\)

where \(a\gt 0\) and \(b\gt 0\), solve this equation for \(b\), giving your answers in terms of \(a\).

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