What is 6ln(x)-1/4 ln(y) ?

The solution to 6ln(x)-1/4 ln(y) is ln((x^6y^{3/4})/y)

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simplify 6ln(x)-1/4 ln(y)

simplify

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

ln (\frac{x ^{6} y ^{\frac{3}{4}}}{y})

Solution steps

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

Apply log rule:

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

6 ln (x) = ln (x^{6})

= ln (x^{6}) - \frac{1}{4} ln (y)

Apply log rule:

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

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

= ln (x^{6}) - ln (y^{\frac{1}{4}})

Apply log rule:

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

ln (x^{6}) - ln (y^{\frac{1}{4}}) = ln (\frac{x ^{6}}{y ^{\frac{1}{4}}})

= ln (\frac{x ^{6}}{y ^{\frac{1}{4}}})

Simplify

\frac{x ^{6}}{y ^{\frac{1}{4}}} : \frac{x ^{6} y ^{\frac{3}{4}}}{y}

= ln (\frac{x ^{6} y ^{\frac{3}{4}}}{y})

\frac{1}{2} lo g_{10} (y) + 2 lo g_{10} (x)

lo g_{2} (\frac{x ^{3}}{y ^{6}})

lo g_{10} (\frac{y}{10000})

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

\frac{2}{3} lo g_{a} (- 2 lo g_{b} (- \frac{1}{5} lo g_{c} (x)))

What is 6ln(x)-1/4 ln(y) ?
The solution to 6ln(x)-1/4 ln(y) is ln((x^6y^{3/4})/y)