What is 8log_{2}(x)-1/4*log_{2}(y) ?

The solution to 8log_{2}(x)-1/4*log_{2}(y) is log_{2}((x^8y^{3/4})/y)

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simplify 8log_{2}(x)-1/4*log_{2}(y)

simplify

8 lo g_{2} (x) - \frac{1}{4} \cdot lo g_{2} (y)

lo g_{2} (\frac{x ^{8} y ^{\frac{3}{4}}}{y})

Solution steps

8 lo g_{2} (x) - \frac{1}{4} lo g_{2} (y)

Apply log rule:

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

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

= lo g_{2} (x^{8}) - \frac{1}{4} lo g_{2} (y)

Apply log rule:

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

\frac{1}{4} lo g_{2} (y) = lo g_{2} (y^{\frac{1}{4}})

= lo g_{2} (x^{8}) - lo g_{2} (y^{\frac{1}{4}})

Apply log rule:

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

lo g_{2} (x^{8}) - lo g_{2} (y^{\frac{1}{4}}) = lo g_{2} (\frac{x ^{8}}{y ^{\frac{1}{4}}})

= lo g_{2} (\frac{x ^{8}}{y ^{\frac{1}{4}}})

Simplify

\frac{x ^{8}}{y ^{\frac{1}{4}}} : \frac{x ^{8} y ^{\frac{3}{4}}}{y}

= lo g_{2} (\frac{x ^{8} y ^{\frac{3}{4}}}{y})

ln (\frac{u - 1}{u + 1})

2 ln (2) + 2 ln (3)

- 3 ln (3) + 6 ln (2)

ln (8) + ln (6) - ln (12)

ln (\frac{x ^{2}}{y ^{5}})

What is 8log_{2}(x)-1/4*log_{2}(y) ?
The solution to 8log_{2}(x)-1/4*log_{2}(y) is log_{2}((x^8y^{3/4})/y)