3.30: Logarithmic exponential and log equations

0606/21/O/N/21 — Question 7 · 9 marks · Exponentials, Log laws, Equations

(a)
Use logarithms to solve 5x+2=3×22x+35^{x + 2} = 3 \times 2^{2x + 3}, giving your answer correct to 11 decimal place.
[4]
(b)
Solve the equation log⁡3(y+11)−2=log⁡3(y−1)\log_{3}(y + 11) - 2 = \log_{3}(y - 1).
[5]