`log(4(x^2)y)` Use the properties of logarithms to expand the expression as a sum, difference, and or constant multiple of logarithms. (Assume all variables are positive.)

Textbook Question

Chapter 3, 3.3 - Problem 46 - Precalculus (3rd Edition, Ron Larson).
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loves2learn | (Level 3) Salutatorian

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Since all of the terms are multiplied, one can just expand by adding them all.

Given,

`log(4x^2y) `

Then,

Separate all of the terms and bring the exponents down in front where necessary.

`log(4x^2y)=log4+2logx+logy `

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