What is 2ln(x)-1/7 ln(y) ?

The solution to 2ln(x)-1/7 ln(y) is ln((x^2y^{6/7})/y)

Popular >

simplify 2ln(x)-1/7 ln(y)

simplify

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

ln (\frac{x ^{2} y ^{\frac{6}{7}}}{y})

Solution steps

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

Apply log rule:

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

2 ln (x) = ln (x^{2})

= ln (x^{2}) - \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^{2}) - ln (y^{\frac{1}{7}})

Apply log rule:

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

ln (x^{2}) - ln (y^{\frac{1}{7}}) = ln (\frac{x ^{2}}{y ^{\frac{1}{7}}})

= ln (\frac{x ^{2}}{y ^{\frac{1}{7}}})

Simplify

\frac{x ^{2}}{y ^{\frac{1}{7}}} : \frac{x ^{2} y ^{\frac{6}{7}}}{y}

= ln (\frac{x ^{2} y ^{\frac{6}{7}}}{y})

lo g_{b} (\frac{1}{10}) + lo g_{b} (50)

lo g_{2} (5) + lo g_{2} (x)

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

\frac{1}{2} (lo g_{7} (r - 2) - lo g_{7} (r))

lo g_{b} (x^{2}) y

What is 2ln(x)-1/7 ln(y) ?
The solution to 2ln(x)-1/7 ln(y) is ln((x^2y^{6/7})/y)