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

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Answer 1 · 2016-04-30T12:24:25

$2 ln x - 2 ln y$ $2lnx-2lny$

The first law of logs you will want to use is $ln (\frac{a}{b}) = ln a - ln b$ $ln(a/b)=lna-lnb$ , so

$ln (\frac{x^{2}}{y^{2}}) = {ln x}^{2} - {ln y}^{2}$ $ln(x^2/y^2)=lnx^2-lny^2$

Another law of logs is that an exponent inside the log is the same as a coefficient outside, or ${ln c}^{2} = 2 ln c$ $lnc^2=2lnc$ , so

${ln x}^{2} - {ln y}^{2} = 2 ln x - 2 ln y$ $lnx^2-lny^2=2lnx-2lny$

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