Express the given quantity as a single logarithm.1/3 \In(x + 2)3 + 1/2

Armorikam

Armorikam

Answered question

2021-10-27

Express the given quantity as a single logarithm.
13ln(x+2)3+12[lnxln(x2+3x+2)2]

Answer & Explanation

SabadisO

SabadisO

Skilled2021-10-28Added 108 answers

(3)13ln(x+2)+12[lnx2ln(x2+3x+2)] The first step is to bring the exponents that can cancel out (all of them in this case) down so that they are multipliers.
ln(x+2)+lnx12ln(x2+3x+2) Simplify the multiplication.
ln[(x+2)(x12)]ln(x2+3x+2) When adding logs of the same base, ypu multiply their insides.
ln(x+2)(x12)(x2+3x+2) When subtracting logs of the same base, divide their insides.
ln(x+2)(x12)(x+2)(x+1) Factor the denominator so you can possibly reduce.
ln(x12)(x+1) Cancel out x+2 from the numerator and the denominator.
Results:
ln(x12)(x+1)

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