Target Mathematics

1.52: Logarithmic equations

4PM1/1/January/2016 — Question 10 · 11 marks

Given that 2log⁡yx+2log⁡xy=52\log_y x+2\log_x y=5
(a) show that log⁡yx=12\log_y x=\dfrac12 or log⁡yx=2\log_y x=2. (5)
(b) Hence, or otherwise, solve the equations
xy=27xy=27
2log⁡yx+2log⁡xy=52\log_y x+2\log_x y=5
(6)