3.3: Single lg and equation with reciprocal logs

0606/12/F/M/23 — Question 4 · 8 marks · Log laws, Change of base, Equations

(a)
Write 3lg⁡x−2lg⁡y2−33\lg x - 2\lg y^{2} - 3 as a single logarithm to base 1010.
[3]
(b)
Solve the equation log⁡3x+log⁡x3=52\log_{3} x + \log_{x} 3 = \dfrac{5}{2}.
[5]