3.32: Fractional powers and lg equation

0606/12/M/J/23 — Question 5 · 10 marks

(a)
Find the exact solutions of 6p2/3−13p1/3−5=06p^{2/3} - 13p^{1/3} - 5 = 0.
[4]
(b)
Solve lg⁡(2x+5)2−lg⁡(x+2)=1\lg(2x + 5)^{2} - \lg(x + 2) = 1, giving answers in exact form.
[6]