Use the properties of logarithms to expand the following expression as much as p

skeexerxo175o

skeexerxo175o

Answered question

2021-11-08

Use the properties of logarithms to expand the following expression as much as possible. Simplify any numerical expressions that can be evaluated without a calculator.
log4(48x+16y)

Answer & Explanation

Helen Rodriguez

Helen Rodriguez

Beginner2021-11-09Added 9 answers

Step 1: Given
The following expression:
log4(48x+16y)
Step 2: To determine
To expand the following expression using the properties of logarithms.
Let, log4(48x+16y)
Expanding the above equation, we get
log4(48x+16y)=log(48x+16y)log(4){by Change of base formula}
=log(16)(3x+y)log(4)
=log(16)+log(3x+y)log(4){logb(mn)=logb(m)+logb(n)}
=log(16)log(4)+log(3x+y)log(4)
=log4(42)+log4(3x+y){logb(x)=logd(x)logd(b)}
=2log4(4)+log4(3x+y)
=2+log4(3x+y){logb(b)=1}
Step 3
Therefore,
log4(48x+16y)=2+log4(3x+y)

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