Calculus Examples

\ln (x) - \ln (y x)

$\ln (x) - \ln (y x)$

Step 1

Use the quotient property of logarithms,

\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})

$\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

\ln (\frac{x}{y x})

$\ln (\frac{x}{y x})$

Step 2

Cancel the common factor of

x

$x$ .

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Step 2.1

Cancel the common factor.

\ln (\frac{x}{y x})

$\ln (\frac{x}{y x})$

Step 2.2

Rewrite the expression.

\ln (\frac{1}{y})

$\ln (\frac{1}{y})$

\ln (\frac{1}{y})

$\ln (\frac{1}{y})$

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