1.38: Logarithmic Equations and Laws

4PM1/1/June/2019 — Question 9 · 12 marks

(a) Solve the equation
2logp9+3log3p=8.2\log_p 9+3\log_3 p=8.
(6)
Given that
log23=log43k,\log_2 3=\log_4 3^k,
(b) find the value of k\displaystyle k.
(2)
(c) Show that
6xlog4x3xlog235log4x+10log23=log4(x6x536x20).6x\log_4 x-3x\log_2 3-5\log_4 x+10\log_2 3 =\log_4\left(\frac{x^{6x-5}}{3^{6x-20}}\right).
(4)