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Popular >

simplify ln(x^{-1})-ln(x)

Solution

simplify

ln (x^{- 1}) - ln (x)

Solution

- ln (x^{2})

Solution steps

ln (x^{- 1}) - ln (x)

Apply log rule:

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

ln (x^{- 1}) - ln (x) = ln (\frac{x ^{- 1}}{x})

= ln (\frac{x ^{- 1}}{x})

Cancel the common factor:

x^{- 1}

= ln (\frac{1}{x ^{2}})

Apply log rule:

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

= - ln (x^{2})

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Frequently Asked Questions (FAQ)

What is ln(x^{-1})-ln(x) ?
The solution to ln(x^{-1})-ln(x) is -ln(x^2)