What is 7ln(x)-1/6 ln(y) ?

The solution to 7ln(x)-1/6 ln(y) is ln((x^7y^{5/6})/y)

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simplify 7ln(x)-1/6 ln(y)

simplify

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

ln (\frac{x ^{7} y ^{\frac{5}{6}}}{y})

Solution steps

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

Apply log rule:

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

7 ln (x) = ln (x^{7})

= ln (x^{7}) - \frac{1}{6} ln (y)

Apply log rule:

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

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

= ln (x^{7}) - ln (y^{\frac{1}{6}})

Apply log rule:

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

ln (x^{7}) - ln (y^{\frac{1}{6}}) = ln (\frac{x ^{7}}{y ^{\frac{1}{6}}})

= ln (\frac{x ^{7}}{y ^{\frac{1}{6}}})

Simplify

\frac{x ^{7}}{y ^{\frac{1}{6}}} : \frac{x ^{7} y ^{\frac{5}{6}}}{y}

= ln (\frac{x ^{7} y ^{\frac{5}{6}}}{y})

ln (\frac{cos ( x )}{cos ( x ) - 1})

ln (2) - ln (7)

lo g_{10} (\frac{( x ^{9} y ^{5} )}{( z ^{3} )})

What is 7ln(x)-1/6 ln(y) ?
The solution to 7ln(x)-1/6 ln(y) is ln((x^7y^{5/6})/y)