4.4.2 Logarithms Equation – Example 2 & 3

Example 2
Solve the following equation:
(a)

\log_{\sqrt{y}} 81 - 3 = \log_{\sqrt{y}} 3

$\log_{\sqrt{y}} 81 - 3 = \log_{\sqrt{y}} 3$
(b)

2 \log_{2} x - \log_{2} (\frac{x}{2} - 1) - 4 = 0

$2 \log_{2} x - \log_{2} (\frac{x}{2} - 1) - 4 = 0$

Example 3
Sole the following equation:
(a)

\log_{3} [\log_{2} (2 x - 1)] = 2

$\log_{3} [\log_{2} (2 x - 1)] = 2$
(b)

\log_{16} [\log_{2} (5 x - 4)] = \log_{9} \sqrt{3}

$\log_{16} [\log_{2} (5 x - 4)] = \log_{9} \sqrt{3}$