### Concept (1)

Sometimes we use methods for expanding logarithms in complicated logarithmic terms. Expanding logarithms can be useful for obtaining more simplified terms. When expanding logarithms we use the rules of logarithms, including the power rule, the product rule and the quotient rule. Sometimes we use methods for expanding logarithms when evaluating logarithmic equations.

### Sample Problems (6)

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 log5 25x² √z
###### Problem 1
How to use the laws of logarithms to expand a log of a quotient.

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 log9 (ab)³ 9(c + d)
###### Problem 2
How to use the laws of logarithms to expand a log of a complicated quotient.

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 log4( 64 )⁻³ ∛x⁴ ⋅ y²
###### Problem 3
How to use the laws of logarithms to expand a log of negative powers of a complicated quotient.
###### Problem 4
How to expand logarithmic expressions using products and powers with focus on using the power rule.
###### Problem 5
How to expand logs using the quotients to sums and differences.
###### Problem 6
Connecting fractional roots and radical expressions with expanding logarithmic expressions.