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Popular >

simplify ln(x^{-1})-ln(x^2)

Solution

simplify

ln (x^{- 1}) - ln (x^{2})

Solution

- ln (x^{3})

Solution steps

ln (x^{- 1}) - ln (x^{2})

Apply log rule:

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

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

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

Simplify

\frac{x ^{- 1}}{x ^{2}} : \frac{1}{x ^{3}}

= ln (\frac{1}{x ^{3}})

Apply log rule:

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

= - ln (x^{3})

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Frequently Asked Questions (FAQ)

What is ln(x^{-1})-ln(x^2) ?
The solution to ln(x^{-1})-ln(x^2) is -ln(x^3)