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

The solution to log_{a}(x)-1/2 log_{a}(z) is log_{a}((xsqrt(z))/z)

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

simplify

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

lo g_{a} (\frac{x z}{z})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

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

= lo g_{a} (\frac{x z}{z})

4 lo g_{10} (3) - 6 lo g_{10} (2)

lo g_{4} (12 x^{3})

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

3 ln (x) + ln (y)

What is log_{a}(x)-1/2 log_{a}(z) ?
The solution to log_{a}(x)-1/2 log_{a}(z) is log_{a}((xsqrt(z))/z)