IXL - Properties of logarithms: mixed review (Algebra 2 practice)

Expand the logarithm. Assume all expressions exist and are well-defined.

Write your answer as a sum or difference of common logarithms or multiples of common logarithms. The inside of each logarithm must be a distinct constant or variable.

log

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question

Expand the logarithm. Assume all expressions exist and are well-defined.

Write your answer as a sum or difference of base-5 logarithms or multiples of base-5 logarithms. The inside of each logarithm must be a distinct constant or variable.

log

key idea

Product Property:

log

where

and

are positive, and

≠

Quotient Property:

log

–

log

where

and

are positive, and

≠

Power Property:

log

where

and

are positive, and

≠

These properties follow an order of operations:

When
expanding,
use the Quotient and Product Properties first, then the Power Property last.
When rewriting as a single
logarithm,
use the Power Property
first,
then the Product and Quotient Properties last.

solution

Expand the logarithm.

log

Quotient Property

log

–

log

Quotient Property

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Work it out

Not feeling ready yet? These can help:

AA.9Product property of logarithms

AA.10Quotient property of logarithms

AA.11Power property of logarithms

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