3.11: Index form and logarithms to base a

0606/23/M/J/21 — Question 3 · 7 marks · Indices, Log laws, Change of base

(a)
Write x(27xy3)5/381y54\dfrac{x(27xy^{3})^{5/3}}{\sqrt[4]{81y^{5}}} in the form 3a×xb×yc3^{a} \times x^{b} \times y^{c} where aa, bb and cc are constants.
[3]
(b)(i)
Find the value of aa such that 2log⁡a8=322\log_{a} 8 = \dfrac{3}{2}.
[2]
(b)(ii)
Write log⁡a2(3a)\log_{a^{2}}(3a) as a single logarithm to base aa.
[2]