1.22: Find the value of such that (b) Show that (c) Hence solve the equation

4PM1/1/June/2024 — Question 9 · 9 marks

(a) Find the value of a\displaystyle a such that loga8=34\displaystyle \mathrm{log}_a 8 = \frac{3}{4}
(2)
(b) Show that
3xlog2x−4log168+6xlog48−log2x=log2(8x)3x−13x \mathrm{log}_2 x - 4 \mathrm{log}_{16} 8 + 6x \mathrm{log}_4 8 - \mathrm{log}_2 x = \mathrm{log}_2(8x)^{3x-1}
(4)
(c) Hence solve the equation 3xlog2x−4log168+6xlog48−log2x=0\displaystyle 3x \mathrm{log}_2 x - 4 \mathrm{log}_{16} 8 + 6x \mathrm{log}_4 8 - \mathrm{log}_2 x = 0
(3)