What is 1/2 log_{4}(x)-7log_{4}(y) ?

The solution to 1/2 log_{4}(x)-7log_{4}(y) is log_{4}((x^{1/2})/(y^7))

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simplify 1/2 log_{4}(x)-7log_{4}(y)

simplify

\frac{1}{2} lo g_{4} (x) - 7 lo g_{4} (y)

lo g_{4} (\frac{x ^{\frac{1}{2}}}{y ^{7}})

Solution steps

\frac{1}{2} lo g_{4} (x) - 7 lo g_{4} (y)

Apply log rule:

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

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

= lo g_{4} (x^{\frac{1}{2}}) - 7 lo g_{4} (y)

Apply log rule:

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

7 lo g_{4} (y) = lo g_{4} (y^{7})

= lo g_{4} (x^{\frac{1}{2}}) - lo g_{4} (y^{7})

Apply log rule:

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

lo g_{4} (x^{\frac{1}{2}}) - lo g_{4} (y^{7}) = lo g_{4} (\frac{x ^{\frac{1}{2}}}{y ^{7}})

= lo g_{4} (\frac{x ^{\frac{1}{2}}}{y ^{7}})

4 lo g_{b} (m) + lo g_{b} (n)

ln (\frac{1}{2} \cdot x^{0.5} \cdot y^{0.5})

lo g_{5} (25 (x + y)^{5})

ln (\frac{x ^{2} + 1}{( x + 3 ) ( x - 2 )})

What is 1/2 log_{4}(x)-7log_{4}(y) ?
The solution to 1/2 log_{4}(x)-7log_{4}(y) is log_{4}((x^{1/2})/(y^7))