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Calculus/rewriting logarithmic equations

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Expert: - 9/22/2010


Question
How do i rewrite the expression as the logarithm of a single quantity?

1/2[ln(x+1)+2ln(x-1)]+3lnx

Answer
If the equation is [ln(x+1) + 2*ln(x-1)]/2 + 3lnx,
this become ln(x+1)/2 + ln(x-1) + 3ln(x).

Numbers out in front of logs can be converted to exponets,
so this is ln√(x+1) + ln(x+1) + ln(x³).

It is then known that these can be combined by
ln(a) + ln(b) + ln(c) = ln(abc) where
a = √(x+1), b = (x+1), and c = x³.

Calculus

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