3.4: Log laws for a and reciprocal-base equation

0606/12/F/M/24 — Question 2 · 7 marks · Log laws, Change of base, Equations

(a)
Given that logpa+logp12logp6=3logp4\log_{p} a + \log_{p} 12 - \log_{p} 6 = 3\log_{p} 4, find the value of aa.
[3]
(b)
Find the exact solutions of the equation 4log3x=9logx34\log_{3} x = 9\log_{x} 3.
[4]