Question

Express the given quantity as a single logarithm. 1 9 ln(x 2)9 1 2 ln x − ln(x2 3x 2)2

Answer 1

The quantity taht should be expresses as a single logarithm is :
1/9 ln(x + 2)^9 + 1/2[ln x − ln(x2 + 3x + 2)^2]
= ln[(x+2)^9]^(1/9) + ln(x^1/2) - ln(x^2+3x+2)
= ln(x+2) + ln(x^(1/2)) - ln(x^2+3x+2)
= ln[(x^(1/2)*(x+2)/(x^2+3x+2)]
= ln[x^(1/2)/(x+1)]