Use the Laws of Logarithms to expand the expression. \log_3\frac{\sqrt{3x

ankarskogC

ankarskogC

Answered question

2021-10-11

Use the Laws of Logarithms to expand the expression.
log33x5y

Answer & Explanation

Khribechy

Khribechy

Skilled2021-10-12Added 100 answers

Step 1
The given logarithm expression can be expanded using following properties of logarithms. The exponent property is logaxy=ylogax
The sum property of logarithms is logax+logay=logaxy. The difference property of logarithms is logaxlogay=logaxy
Step 2
The given expression is log33x5y. Use the properties of logarithms to expand the expression.
log33x5y=log33x5log3y
=log3(3x5)12log3y
=12log3(3x5)log3y
=12(log33+log3x5)log3y
=12(1+5log3x)log3y
=12+52log3xlog3y

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