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

The solution to 2ln(x)-1/5 ln(y) is ln((x^2y^{4/5})/y)

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

simplify

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

ln (\frac{x ^{2} y ^{\frac{4}{5}}}{y})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{x ^{2}}{y ^{\frac{1}{5}}} : \frac{x ^{2} y ^{\frac{4}{5}}}{y}

= ln (\frac{x ^{2} y ^{\frac{4}{5}}}{y})

lo g_{7} (2 x)

lo g_{b} (x + 1) + lo g_{b} (3) - lo g_{b} (x + 2)

lo g_{4} (\frac{16}{x + 9})

ln (\frac{x ^{2} - 1}{x ^{3}})

4 lo g_{2} (u) + 7 lo g_{2} (v)

What is 2ln(x)-1/5 ln(y) ?
The solution to 2ln(x)-1/5 ln(y) is ln((x^2y^{4/5})/y)