What is 7log_{2}(x)-1/3 log_{2}(y) ?

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

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simplify 7log_{2}(x)-1/3 log_{2}(y)

simplify

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

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

Solution steps

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

Apply log rule:

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

7 lo g_{2} (x) = lo g_{2} (x^{7})

= lo g_{2} (x^{7}) - \frac{1}{3} lo g_{2} (y)

Apply log rule:

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

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

= lo g_{2} (x^{7}) - lo g_{2} (y^{\frac{1}{3}})

Apply log rule:

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

lo g_{2} (x^{7}) - lo g_{2} (y^{\frac{1}{3}}) = lo g_{2} (\frac{x ^{7}}{y ^{\frac{1}{3}}})

= lo g_{2} (\frac{x ^{7}}{y ^{\frac{1}{3}}})

Simplify

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

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

lo g_{10} (2) + lo g_{10} (7)

lo g_{b} (\frac{x}{3})

ln (x^{2} - 13 x + 36) + 2 ln (x - 4) - ln (x - 9)

lo g_{6} (\frac{216}{y})

4 lo g_{10} (x y) - 3 lo g_{10} (yz)

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