3.52: Log domain and exact equation

0606/21/M/J/21 — Question 8 · 4 marks

In this question, aa, bb, cc and dd are positive constants.
(a)(i)
It is given that y=log⁡a ⁣(x−12)+log⁡a(x+2)y = \log_{a}\!\left(x - \tfrac{1}{2}\right) + \log_{a}(x + 2). Explain why xx must be greater than 12\tfrac{1}{2}.
[1]
(a)(ii)
Find the exact solution of the equation y+log⁡a3=log⁡a6y + \log_{a} 3 = \log_{a} 6.
[3]