Calculate the value of each of the following logarithms

MATHEMATICS · Multi-part · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

Calculate the value of each of the following logarithms. It is given that

\log_{ab} a = 3

, where

a, b \in \mathbb{R}^{+}

and

ab \ne 1

. (1)

\log_2 \frac{1}{16}

. (2)

\log_9 3

. (3)

\log_{\sqrt{3}} 81

. (4) Show that

\log_{ab} b = -2

. (5) Hence find the value of

\log_{ab} \frac{\sqrt[3]{a}}{\sqrt{b}}