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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{10} (x) + lo g_{10} (y^{\frac{1}{2}}) = lo g_{10} (x y^{\frac{1}{2}})

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2400 \cdot ln (\frac{750}{750 - 14 ( t )}) - (9.81 \cdot t)

5 lo g_{6} (u) + 2 lo g_{6} (v)

3 lo g_{4} (u) - 18 lo g_{4} (v)

\frac{lo g _{10} ( 2 )}{lo g _{10} ( 5 ) - lo g _{10} ( 2 )}

ln (\frac{8}{10})

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