# Evaluating logarithms using logarithm rules

### Evaluating logarithms using logarithm rules

#### Lessons

• Introduction
A Summary of Logarithm Rules

• 1.
a)
Which of the following correctly states the
"product law"?
i)
$\log_2 8 + \log_2 4 = \log_2 12$
ii)
$\log_2 8 + \log_2 4 = \log_2 32$
iii)
$\log_2 8 \cdot \log_2 4 = \log_2 32$

b)
Which of the following correctly states the
"quotient law"?
i)
$\log_b 15 - \log_b 3 = \log_b 5$
ii)
$\log_b 15 - \log_b 3 = \log_b 12$
iii)
${{\log_b \sqrt{8}} \over {\log_b \sqrt{32}}} = \log_b(\sqrt{1 \over 4})$

c)
Which of the following correctly states the
"power law"?
i)
$(\log 100)^3 = \log 100^3$
ii)
$(\log 100)^3 = 3\log 100$
iii)
$\log 100^3 = 3\log 100$

• 2.
Evaluate and state the laws involved in each step of
the calculation:
${5 \log_2{^3}\sqrt{80} \over 5 \log_2{^3}\sqrt{20}}$

• 3.
Express as a single logarithm:

${\log A-3\log B-\log C}$

• 4.
Evaluate logarithms:
a)
Determine the value of ${\log_n ab^2, }$
if ${\log_na=5}$ and ${\log_nb=3}$

b)
Given: $\log_5x = y$
express$\log_5125{x^4}$

• 5.
Evaluate.
a)
$\log_3 \sqrt{15}- {1\over2} \log_35$

b)
$\frac{({a^{\log_a8})}({a^{\log_a3}})}{a^{\log_a6}}$

• 6.
a)
If ${\log_3x^2 = 2}$ and ${2\log_b\sqrt{x} = {1\over3},}$
then the value of $b$ is ____________________ .

b)
If ${\log_5x^2 = 4}$ and ${\log_2y^3 = 6 ,}$ and ${\log_bx+\log_by = {1\over2}}$ where x, y > 0,
then the value of b is ____________________ .