Quotient Rule of Logarithms - Concept

Concept Concept (1)

When evaluating logarithms the logarithmic rules, such as the quotient rule of logarithms, can be useful for rewriting logarithmic terms. The quotient rule of logarithms allows us to separate parts of a quotient within a log. The quotient rule of logarithms is useful for expanding and condensing logarithms, along with the product rule and the power rule of logarithms.

Sample Sample Problems (4)

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Quotient Rule of Logarithms - Problem 1

Simplify:

log7(49⁄3)
Problem 1
How to use the quotient rule for logarithms to break up a log.
Quotient Rule of Logarithms - Problem 2

Simplify:

log5x − log5(x + 3)
Problem 2
How to use the quotient rule for logarithms to condense a difference.
Quotient Rule of Logarithms - Problem 3

logb(x⁄y) = logbx − logby

Let m = logbx and n = logby
Problem 3
How to prove the quotient rule for logarithms.
Quotient Rule of Logarithms - Problem 4
Problem 4
How to expand and condense logs with the same base using the quotient rule.