3.17: Single lg and quadratic in log_c 3

0606/13/M/J/23 — Question 3 · 8 marks · Log laws, Change of base, Equations

(a)

Write

3 + 2\lg a - \dfrac{1}{2}\lg(4b^{2})

, where

a

and

b

are both positive, as a single logarithm to base

10

. Give your answer in its simplest form.

[3]

(b)

Given that

2\log_{c} 3 = 7 + 4\log_{3} c

, find the possible values of the positive constant

c

, giving your answers in exact form.

[5]