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Popular >

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

Solution

simplify

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

Solution

- ln (x^{4} y^{2})

Solution steps

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

Apply log rule:

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

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

= ln ((x^{- 2})^{2}) - ln (y^{2})

Apply log rule:

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

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

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

Simplify

\frac{( x ^{- 2} ) ^{2}}{y ^{2}} : \frac{1}{x ^{4} y ^{2}}

= ln (\frac{1}{x ^{4} y ^{2}})

Apply log rule:

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

= - ln (x^{4} y^{2})

Apply exponent rule:

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

x^{4} y^{2} = (x^{2} y)^{2}

= - ln ((x^{2} y)^{2})

(x^{2} y)^{2} = x^{4} y^{2}

= - ln (x^{4} y^{2})

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Frequently Asked Questions (FAQ)

What is 2ln(x^{-2})-ln(y^2) ?
The solution to 2ln(x^{-2})-ln(y^2) is -ln(x^4y^2)