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Popular >

simplify ln(x^{-5})-5ln(y)

Solution

simplify

ln (x^{- 5}) - 5 ln (y)

Solution

- ln (x^{5} y^{5})

Solution steps

ln (x^{- 5}) - 5 ln (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

5 ln (y) = ln (y^{5})

= ln (x^{- 5}) - ln (y^{5})

Apply log rule:

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

ln (x^{- 5}) - ln (y^{5}) = ln (\frac{x ^{- 5}}{y ^{5}})

= ln (\frac{x ^{- 5}}{y ^{5}})

Simplify

\frac{x ^{- 5}}{y ^{5}} : \frac{1}{x ^{5} y ^{5}}

= ln (\frac{1}{x ^{5} y ^{5}})

Apply log rule:

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

= - ln (x^{5} y^{5})

Apply exponent rule:

a^{m} b^{m} = (ab)^{m}

x^{5} y^{5} = (x y)^{5}

= - ln ((x y)^{5})

(x y)^{5} = x^{5} y^{5}

= - ln (x^{5} y^{5})

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Frequently Asked Questions (FAQ)

What is ln(x^{-5})-5ln(y) ?
The solution to ln(x^{-5})-5ln(y) is -ln(x^5y^5)