# Combining product rule and quotient rule in logarithms

### Combining product rule and quotient rule in logarithms

#### Lessons

$\log [A \cdot B \div C \div D \cdot E] = \log\;A + \log\;B - \log\;C - \log\;D + \log\;E$
• 1.
Evaluate:
a)
$\log_5 60 - \log_5 3 + \log_5 5 - \log_5 20$

b)
given:
${{a \over {bc}} = 9}$
ask: $5\log_3 a - 5\log_3 b - 5\log_3 c$

c)
if $\log_a x = 3$ and $\log_a y = 4,$
evaluate $(\log_a {1 \over xy})^2$

• 2.
Simplify $\log 5a^3 - \log b^2 + \log {2b \over c} + \log b - \log{a^3 \over 100}$