3.31: Three logarithmic/exponential equations

0606/23/O/N/21 — Question 4 · 8 marks · Log laws, Exponentials, Equations

(a)
Solve the equation log⁡2(2x−3)=4\log_{2}(2x - 3) = 4. Give your answer in exact form.
[2]
(b)
Solve the equation ln⁡2u−ln⁡(u−4)=1\ln 2u - \ln(u - 4) = 1. Give your answer in exact form.
[3]
(c)
Solve the equation 27v=92v−527^{v} = 9^{2v - 5}.
[3]