4.03: Logarithmic manipulation and equation

0606/12/M/J/26 — Question 9 · 7 marks

(a)
Write \(\dfrac{1}{\log_xe}-\ln(x-1)\) as a single logarithm.
[2]
(b)
Solve \(2\log_5(2x)=1+\log_5(9x-10)\).
[5]