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Popular >

simplify ln(x/y)-ln(x)

Solution

simplify

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

Solution

- ln (y)

Solution steps

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

Simplify

\frac{\frac{x}{y}}{x} : \frac{1}{y}

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

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (y)

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Frequently Asked Questions (FAQ)

What is ln(x/y)-ln(x) ?
The solution to ln(x/y)-ln(x) is -ln(y)