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

Question

Morris

Mathematics

17 April, 00:56

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

+1

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Eliezer Fuentes · 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]

= l n[ (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)

= l n[ (x^ (1/2) * (x+2) / (x^2+3x+2) ]

= ln[x^ (1/2) / (x+1) ]