What is 3log_{10}(x)-1/2 log_{10}(z) ?

The solution to 3log_{10}(x)-1/2 log_{10}(z) is log_{10}((x^3sqrt(z))/z)

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simplify 3log_{10}(x)-1/2 log_{10}(z)

simplify

3 lo g_{10} (x) - \frac{1}{2} lo g_{10} (z)

lo g_{10} (\frac{x ^{3} z}{z})

Solution steps

3 lo g_{10} (x) - \frac{1}{2} lo g_{10} (z)

Apply log rule:

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

3 lo g_{10} (x) = lo g_{10} (x^{3})

= lo g_{10} (x^{3}) - \frac{1}{2} lo g_{10} (z)

Apply log rule:

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

\frac{1}{2} lo g_{10} (z) = lo g_{10} (z^{\frac{1}{2}})

= lo g_{10} (x^{3}) - lo g_{10} (z^{\frac{1}{2}})

Apply log rule:

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

lo g_{10} (x^{3}) - lo g_{10} (z^{\frac{1}{2}}) = lo g_{10} (\frac{x ^{3}}{z ^{\frac{1}{2}}})

= lo g_{10} (\frac{x ^{3}}{z ^{\frac{1}{2}}})

Simplify

\frac{x ^{3}}{z ^{\frac{1}{2}}} : \frac{x ^{3} z}{z}

= lo g_{10} (\frac{x ^{3} z}{z})

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What is 3log_{10}(x)-1/2 log_{10}(z) ?
The solution to 3log_{10}(x)-1/2 log_{10}(z) is log_{10}((x^3sqrt(z))/z)