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Popular >

simplify ln(xy)-1/2 ln(x^2)

Solution

simplify

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

Solution

ln (y)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

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

= ln (y)

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Frequently Asked Questions (FAQ)

What is ln(xy)-1/2 ln(x^2) ?
The solution to ln(xy)-1/2 ln(x^2) is ln(y)