How do you expand $ln sqrt(x^3/y^2)$ ?

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Answer 1 · 2016-07-26T16:36:50

$3/2*ln x - lny$

$ln sqrt(x^3/y^2)$ can be rewritten as

$ln (x^3/y^2)^(1/2)$

or $ln (x^(3/2)/y^(2/2))$

using one of logarithm rules: $ln (a/b) = lna - lnb$

we have:

$ln x^(3/2) - ln y^(2/2)$

or $ln x^(3/2) - ln y$

another one of these rules state that: $ln a^b = b*lna$

then we have:

$3/2*ln x - lny$

How do you expand ln sqrt(x^3/y^2)ln sqrt(x^3/y^2)?