What is 5ln(x)-1/2 ln(y) ?

The solution to 5ln(x)-1/2 ln(y) is ln((x^5sqrt(y))/y)

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simplify 5ln(x)-1/2 ln(y)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

= ln (x^{5}) - \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^{5}) - ln (y^{\frac{1}{2}})

Apply log rule:

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

ln (x^{5}) - ln (y^{\frac{1}{2}}) = ln (\frac{x ^{5}}{y ^{\frac{1}{2}}})

= ln (\frac{x ^{5}}{y ^{\frac{1}{2}}})

Simplify

\frac{x ^{5}}{y ^{\frac{1}{2}}} : \frac{x ^{5} y}{y}

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

lo g_{b} (\frac{x ^{2} y}{z ^{7}})

\frac{1}{5} ln (2)

3 lo g_{6} (x) + lo g_{6} (y)

lo g_{5} (x^{7})

lo g_{3} (13 z)

What is 5ln(x)-1/2 ln(y) ?
The solution to 5ln(x)-1/2 ln(y) is ln((x^5sqrt(y))/y)