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

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Answer 1 · 2016-07-26T16:36:50

$\frac{3}{2} \cdot ln x - ln y$ $3/2*ln x - lny$

$ln \sqrt{\frac{x^{3}}{y^{2}}}$ $ln sqrt(x^3/y^2)$ can be rewritten as

${ln (\frac{x^{3}}{y^{2}})}^{\frac{1}{2}}$ $ln (x^3/y^2)^(1/2)$

or $ln (\frac{x^{\frac{3}{2}}}{y^{\frac{2}{2}}})$ $ln (x^(3/2)/y^(2/2))$

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

we have:

${ln x}^{\frac{3}{2}} - {ln y}^{\frac{2}{2}}$ $ln x^(3/2) - ln y^(2/2)$

or ${ln x}^{\frac{3}{2}} - ln y$ $ln x^(3/2) - ln y$

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

then we have:

$\frac{3}{2} \cdot ln x - ln y$ $3/2*ln x - lny$

How do you expand ln sqrt(x^3/y^2)ln√x3y2ln sqrt(x^3/y^2)?