Use the Properties of Logarithms to condense the logarithm. Simplify if possible

Grady Turner

Grady Turner

Answered question

2021-11-07

Use the Properties of Logarithms to condense the logarithm. Simplify if possible. (Assume the variable is positive.)
log3(x21)2log3(x1)

Answer & Explanation

Uersfeldte

Uersfeldte

Beginner2021-11-08Added 20 answers

Step 1
To simplify: log3(x21)2log3(x1) by the use of Properties of Logarithms.
Formula used:
Logarithmic properties.
1. alogc(b)=logc(ba)
2. logc(a)logc(b)=logc(ab)
Step 2
Calculation:
Apply log rule alogc(b)=logc(ba)
log3(x21)2log3(x1)=log3(x21)log3((x1)2)
Now apply the log rule logc(a)logc(b)=logc(ab)
log3(x21)log3((x1)2)=log3(x21(x1)2)
log3(x21)log3((x1)2)=log3(x21(x1)2)
=log3((x+1)(x1)(x1)2)
=log3(x+1x1)
Step 3
Answer:
log3(x21)log3((x1)2)=log3(x+1x1)

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