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

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

Popular >

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

lo g_{b} (\frac{x ^{3} y}{z ^{8}})

- \frac{1}{2} ln ∣ u ∣ + \frac{1}{2} ln ∣ u - 2 ∣

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

lo g_{π} (\frac{π ^{3} x ^{4} y ^{5} z}{( x - 1 ) ^{2} z})

ln (\frac{s}{s + 1})

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