# Evaluating logarithms using logarithm rules

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### Introduction

#### Lessons

1. A Summary of Logarithm Rules
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### Examples

#### Lessons

1. 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)
$\log_2 8 \cdot \log_2 4 = \log_2 32$
2. 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)
${{\log_b \sqrt{8}} \over {\log_b \sqrt{32}}} = \log_b(\sqrt{1 \over 4})$
3. 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:
${5 ^{log_2{^3}\sqrt{80}} \over 5 ^{log_2{^3}\sqrt{20}}}$
1. Express as a single logarithm:

${\log A-3\log B-\log C}$
1. Evaluate logarithms:
1. Determine the value of ${\log_n ab^2, }$
if ${\log_na=5}$ and ${\log_nb=3}$
2. Given: $\log_5x = y$
express$\log_5125{x^4}$
2. Evaluate.
1. $\log_3 \sqrt{15}- {1\over2} \log_35$
2. $\frac{({a^{\log_a8})}({a^{\log_a3}})}{a^{\log_a6}}$
1. If ${\log_3x^2 = 2}$ and ${2\log_b\sqrt{x} = {1\over3},}$
then the value of $b$ is ____________________ .
2. 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 ____________________ .

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