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

The solution to 7ln(x)-1/3 ln(y) is ln((x^7y^{2/3})/y)

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

simplify

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

ln (\frac{x ^{7} y ^{\frac{2}{3}}}{y})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{x ^{7}}{y ^{\frac{1}{3}}} : \frac{x ^{7} y ^{\frac{2}{3}}}{y}

= ln (\frac{x ^{7} y ^{\frac{2}{3}}}{y})

ln (x^{6} 7 - x)

- lo g_{10} (7.9 \cdot 1 0^{- 9})

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

f (x) = ln (\frac{3 ^{x} 6 ^{3 x}}{2 ^{3 x}})

\frac{1}{2} lo g_{10} (x) - lo g_{10} (2) - 7 lo g_{10} (m)

What is 7ln(x)-1/3 ln(y) ?
The solution to 7ln(x)-1/3 ln(y) is ln((x^7y^{2/3})/y)