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

The solution to 7ln(x)-1/4 ln(y) is ln((x^7y^{3/4})/y)

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

simplify

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

ln (\frac{x ^{7} y ^{\frac{3}{4}}}{y})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{x ^{7}}{y ^{\frac{1}{4}}} : \frac{x ^{7} y ^{\frac{3}{4}}}{y}

= ln (\frac{x ^{7} y ^{\frac{3}{4}}}{y})

lo g_{8} (64 x^{2})

5 lo g_{2} (5) + 5 lo g_{2} (7) - 15 lo g_{2} (6)

ln (\frac{1 + 2 x}{1 - x})

lo g_{b} (x^{2} y^{3})

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

What is 7ln(x)-1/4 ln(y) ?
The solution to 7ln(x)-1/4 ln(y) is ln((x^7y^{3/4})/y)