What is log_{b}(x)+3log_{b}(y)-1/2 log_{b}(z) ?

The solution to log_{b}(x)+3log_{b}(y)-1/2 log_{b}(z) is log_{b}((xy^3sqrt(z))/z)

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simplify log_{b}(x)+3log_{b}(y)-1/2 log_{b}(z)

simplify

lo g_{b} (x) + 3 lo g_{b} (y) - \frac{1}{2} lo g_{b} (z)

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

Solution steps

lo g_{b} (x) + 3 lo g_{b} (y) - \frac{1}{2} lo g_{b} (z)

Apply log rule:

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

3 lo g_{b} (y) = lo g_{b} (y^{3})

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{b} (x) + lo g_{b} (y^{3}) = lo g_{b} (x y^{3})

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

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

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

ln (e (x + 9))

lo g_{10} (m) - lo g_{10} (n) + lo g_{10} (p)

ln (\frac{x}{1 + x})

lo g_{a} (7 x - 4) - lo g_{a} (5 x + 2)

- lo g_{10} (1.6 \cdot 1 0^{- 5})

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