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

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

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

simplify

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

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

Solution steps

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

2 lo g_{4} (x) = lo g_{4} (x^{2})

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

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

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

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

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

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

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

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

Simplify

\frac{\frac{x ^{2}}{y}}{z ^{\frac{1}{2}}} : \frac{x ^{2}}{y z ^{\frac{1}{2}}}

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

Apply exponent rule:

a^{\frac{1}{2}} = a

z^{\frac{1}{2}} = z

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

lo g_{5} (\frac{3 x + 2}{x + 1})

ln (\frac{e ^{x l n (2)}}{2})

lo g_{10} (1000 y)

ln (3 e^{x})

ln (\frac{π}{4})

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