What is 3ln(x)-1/7 ln(y) ?

The solution to 3ln(x)-1/7 ln(y) is ln((x^3y^{6/7})/y)

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simplify 3ln(x)-1/7 ln(y)

simplify

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

ln (\frac{x ^{3} y ^{\frac{6}{7}}}{y})

Solution steps

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

Apply log rule:

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

3 ln (x) = ln (x^{3})

= ln (x^{3}) - \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^{3}) - ln (y^{\frac{1}{7}})

Apply log rule:

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

ln (x^{3}) - ln (y^{\frac{1}{7}}) = ln (\frac{x ^{3}}{y ^{\frac{1}{7}}})

= ln (\frac{x ^{3}}{y ^{\frac{1}{7}}})

Simplify

\frac{x ^{3}}{y ^{\frac{1}{7}}} : \frac{x ^{3} y ^{\frac{6}{7}}}{y}

= ln (\frac{x ^{3} y ^{\frac{6}{7}}}{y})

\frac{1}{2} ln (x) + 8 ln (y) - 5 ln (z)

\frac{1}{2} ln (x) + 4 ln (y) - 9 ln (z)

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

lo g_{10} (\frac{x}{100 y ^{5}})

What is 3ln(x)-1/7 ln(y) ?
The solution to 3ln(x)-1/7 ln(y) is ln((x^3y^{6/7})/y)