What is log_{10}((x^6y^8)/(z^{10)}) ?

The solution to log_{10}((x^6y^8)/(z^{10)}) is 6log_{10}(x)+8log_{10}(y)-10log_{10}(z)

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simplify log_{10}((x^6y^8)/(z^{10)})

simplify

lo g_{10} (\frac{x ^{6} y ^{8}}{z ^{10}})

6 lo g_{10} (x) + 8 lo g_{10} (y) - 10 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{x ^{6} y ^{8}}{z ^{10}})

Apply log rule:

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

lo g_{10} (\frac{x ^{6} y ^{8}}{z ^{10}}) = lo g_{10} (x^{6} y^{8}) - lo g_{10} (z^{10})

= lo g_{10} (x^{6} y^{8}) - lo g_{10} (z^{10})

lo g_{10} (x^{6} y^{8}) = 6 lo g_{10} (x) + 8 lo g_{10} (y)

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

= 6 lo g_{10} (x) + 8 lo g_{10} (y) - 10 lo g_{10} (z)

ln (\frac{100}{x})

- lo g_{y} (\frac{1}{12})

lo g_{a} (\frac{3}{5})

5 ln (\frac{2}{3})

lo g_{8} (m n^{2})

What is log_{10}((x^6y^8)/(z^{10)}) ?
The solution to log_{10}((x^6y^8)/(z^{10)}) is 6log_{10}(x)+8log_{10}(y)-10log_{10}(z)