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Overview
ALEKS Exponentials and Trigonometry
Logarithmic functions
5. Logarithm rules
5.7 Combining the laws of logarithms
Combining the Laws of Logarithms (Condensing and Expanding)
See how the product, quotient, and power laws let you condense several logarithms into one, or expand a single log into many.
What You'll Learn
Combining logarithms means using the product, quotient, and power laws together to merge several log terms into one expression
The product law turns log base b of x plus log base b of y into log base b of the product x times y
The quotient law turns log base b of x minus log base b of y into log base b of the quotient x divided by y
The power law lets an exponent in front of a log move inside as an exponent, or the reverse
Condensing a logarithmic expression and expanding one are reverse processes that rely on the exact same three laws
Every law only applies when all logs share the same base and every argument stays positive
This Unit Includes
Learning resources
TEST-PREP Curriculum Aligned