Condense the expression 3\ln x + 2\ln(x + 1) to the logarithm of a single

coexpennan

coexpennan

Answered question

2021-10-24

Condense the expression 3lnx+2ln(x+1) to the logarithm of a single quantity.

Answer & Explanation

au4gsf

au4gsf

Skilled2021-10-25Added 95 answers

Step 1 Background Concept
The logarithms have the following properties.
lnxa=alnx
ln(ab)=lna+lnb
ln(ab)=lnalnb
Given logarithm expression:
3lnx+2ln(x+1)
Step 2 Use the properties of logarithms to condense the given equation
The given equation can be condensed to single quantity by following the given steps.
Use the follwing property of logarithms.
lnxa=alnx
The equation now becomes,
3lnx+2ln(x+1)=lnx3+ln(x+1)2
Now, use,
ln(ab)=lna+lnb
The equation finally becomes,
3lnx+2ln(x+1)=lnx3+ln(x+1)2=ln(x3(x+1)2)

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