What is log_{10}((x^9y^5)/(z^3)) ?

The solution to log_{10}((x^9y^5)/(z^3)) is 9log_{10}(x)+5log_{10}(y)-3log_{10}(z)

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simplify log_{10}((x^9y^5)/(z^3))

simplify

lo g_{10} (\frac{x ^{9} y ^{5}}{z ^{3}})

9 lo g_{10} (x) + 5 lo g_{10} (y) - 3 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{x ^{9} y ^{5}}{z ^{3}})

Apply log rule:

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

lo g_{10} (\frac{x ^{9} y ^{5}}{z ^{3}}) = lo g_{10} (x^{9} y^{5}) - lo g_{10} (z^{3})

= lo g_{10} (x^{9} y^{5}) - lo g_{10} (z^{3})

lo g_{10} (x^{9} y^{5}) = 9 lo g_{10} (x) + 5 lo g_{10} (y)

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

= 9 lo g_{10} (x) + 5 lo g_{10} (y) - 3 lo g_{10} (z)

ln (x - 1) - ln (x + 8)

lo g_{10} (x) - 4 lo g_{10} (y) + 7 lo g_{10} (z)

ln (1) - ln (7 e^{- x})

lo g_{5} (\frac{a ^{3}}{b ^{2}})

\frac{1}{2} (lo g_{6} (x) + lo g_{6} (y))

What is log_{10}((x^9y^5)/(z^3)) ?
The solution to log_{10}((x^9y^5)/(z^3)) is 9log_{10}(x)+5log_{10}(y)-3log_{10}(z)