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

The solution to 5ln(x)-1/5 ln(y) is ln((x^5y^{4/5})/y)

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

simplify

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

ln (\frac{x ^{5} y ^{\frac{4}{5}}}{y})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{x ^{5}}{y ^{\frac{1}{5}}} : \frac{x ^{5} y ^{\frac{4}{5}}}{y}

= ln (\frac{x ^{5} y ^{\frac{4}{5}}}{y})

- (\frac{2}{14}) lo g_{2} (\frac{2}{14}) - (\frac{3}{14}) lo g_{2} (\frac{3}{14})

lo g_{3} (\frac{9 x ^{4}}{y})

lo g_{m} (a b^{2} c^{3})

lo g_{4} (7) + lo g_{4} (11)

lo g_{3} (27) + lo g_{10} (+ \frac{3}{4})

What is 5ln(x)-1/5 ln(y) ?
The solution to 5ln(x)-1/5 ln(y) is ln((x^5y^{4/5})/y)