What is 4ln(x)-1/7 ln(y) ?

The solution to 4ln(x)-1/7 ln(y) is ln((x^4y^{6/7})/y)

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simplify 4ln(x)-1/7 ln(y)

simplify

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

ln (\frac{x ^{4} y ^{\frac{6}{7}}}{y})

Solution steps

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

Apply log rule:

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

4 ln (x) = ln (x^{4})

= ln (x^{4}) - \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^{4}) - ln (y^{\frac{1}{7}})

Apply log rule:

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

ln (x^{4}) - ln (y^{\frac{1}{7}}) = ln (\frac{x ^{4}}{y ^{\frac{1}{7}}})

= ln (\frac{x ^{4}}{y ^{\frac{1}{7}}})

Simplify

\frac{x ^{4}}{y ^{\frac{1}{7}}} : \frac{x ^{4} y ^{\frac{6}{7}}}{y}

= ln (\frac{x ^{4} y ^{\frac{6}{7}}}{y})

lo g_{10} (\frac{x ^{3} ( x + 1 )}{( x - 2 ) ^{2}})

lo g_{5} (x - 3) + lo g_{5} (3 x + 1)

lo g_{10} (25) + lo g_{10} (2) - lo g_{10} (3)

lo g_{6} (\frac{5 x ^{3}}{y})

ln (\frac{4}{17})

What is 4ln(x)-1/7 ln(y) ?
The solution to 4ln(x)-1/7 ln(y) is ln((x^4y^{6/7})/y)