What is 8ln(x)-1/7 ln(y) ?

The solution to 8ln(x)-1/7 ln(y) is ln((x^8y^{6/7})/y)

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simplify 8ln(x)-1/7 ln(y)

simplify

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

ln (\frac{x ^{8} y ^{\frac{6}{7}}}{y})

Solution steps

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

Apply log rule:

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

8 ln (x) = ln (x^{8})

= ln (x^{8}) - \frac{1}{7} ln (y)

Apply log rule:

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

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

= ln (x^{8}) - ln (y^{\frac{1}{7}})

Apply log rule:

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

ln (x^{8}) - ln (y^{\frac{1}{7}}) = ln (\frac{x ^{8}}{y ^{\frac{1}{7}}})

= ln (\frac{x ^{8}}{y ^{\frac{1}{7}}})

Simplify

\frac{x ^{8}}{y ^{\frac{1}{7}}} : \frac{x ^{8} y ^{\frac{6}{7}}}{y}

= ln (\frac{x ^{8} y ^{\frac{6}{7}}}{y})

- \frac{4}{10} lo g_{2} (\frac{4}{10}) - \frac{6}{10} lo g_{2} (\frac{6}{10})

ln (\frac{3 x - 5}{7})

lo g_{49} (\frac{20000}{50}) + 1

lo g_{10} (\frac{7 ( x + 6 ) ^{3}}{x ^{5}})

lo g_{2} (\frac{a ^{2} - 4}{7})

What is 8ln(x)-1/7 ln(y) ?
The solution to 8ln(x)-1/7 ln(y) is ln((x^8y^{6/7})/y)