4.2.2(c) Example 3 (Change of Base of Logarithms)

Example 3
Given that

\log_{3} x = b

$\log_{3} x = b$ , express

\log_{x} 9 x

$\log_{x} 9 x$ in term of b.

Example 4
Given that

\log_{2} 3 = 1.585

$\log_{2} 3 = 1.585$ and

\log_{2} 5 = 2.322

$\log_{2} 5 = 2.322$ , evaluate the following.
(a)

\log_{8} 15

$\log_{8} 15$
(b)

\log_{5} 0.6

$\log_{5} 0.6$
(c)

\log_{15} 30

$\log_{15} 30$
(d)

\log_{16} 45

$\log_{16} 45$

Solution: