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Popular >

simplify 7ln(x)-1/2 ln(y)

Solution

simplify

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

Solution

ln (\frac{x ^{7} y}{y})

Solution steps

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

Apply log rule:

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

7 ln (x) = ln (x^{7})

= ln (x^{7}) - \frac{1}{2} ln (y)

Apply log rule:

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

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

= ln (x^{7}) - ln (y^{\frac{1}{2}})

Apply log rule:

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

ln (x^{7}) - ln (y^{\frac{1}{2}}) = ln (\frac{x ^{7}}{y ^{\frac{1}{2}}})

= ln (\frac{x ^{7}}{y ^{\frac{1}{2}}})

Simplify

\frac{x ^{7}}{y ^{\frac{1}{2}}} : \frac{x ^{7} y}{y}

= ln (\frac{x ^{7} y}{y})

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Frequently Asked Questions (FAQ)

What is 7ln(x)-1/2 ln(y) ?
The solution to 7ln(x)-1/2 ln(y) is ln((x^7sqrt(y))/y)