What is 4ln(x)-1/5 ln(y) ?

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

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simplify 4ln(x)-1/5 ln(y)

simplify

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

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

Solution steps

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

Apply log rule:

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

4 ln (x) = ln (x^{4})

= ln (x^{4}) - \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^{4}) - ln (y^{\frac{1}{5}})

Apply log rule:

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

ln (x^{4}) - ln (y^{\frac{1}{5}}) = ln (\frac{x ^{4}}{y ^{\frac{1}{5}}})

= ln (\frac{x ^{4}}{y ^{\frac{1}{5}}})

Simplify

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

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

lo g_{10} (\frac{3 x}{7})

lo g_{5} (\frac{25}{x + 7})

lo g_{a} (\frac{a B}{C ^{4}})

lo g_{10} (\frac{( 1 + x )}{( 1 - x )})

3 lo g_{10} (4) - 1 lo g_{10} (x)

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