What is log_{10}((x^8y^9)/(z^3)) ?

The solution to log_{10}((x^8y^9)/(z^3)) is 8log_{10}(x)+9log_{10}(y)-3log_{10}(z)

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simplify log_{10}((x^8y^9)/(z^3))

simplify

lo g_{10} (\frac{x ^{8} y ^{9}}{z ^{3}})

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

Solution steps

lo g_{10} (\frac{x ^{8} y ^{9}}{z ^{3}})

Apply log rule:

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

lo g_{10} (\frac{x ^{8} y ^{9}}{z ^{3}}) = lo g_{10} (x^{8} y^{9}) - lo g_{10} (z^{3})

= lo g_{10} (x^{8} y^{9}) - lo g_{10} (z^{3})

lo g_{10} (x^{8} y^{9}) = 8 lo g_{10} (x) + 9 lo g_{10} (y)

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

= 8 lo g_{10} (x) + 9 lo g_{10} (y) - 3 lo g_{10} (z)

lo g_{b} (x) + lo g_{b} (x) + lo g_{b} (3)

ln (\frac{1}{2.6})

lo g_{3} (\frac{x ^{2} ( 2 x + 1 )}{x - 2})

5 lo g_{3} (u) + 6 lo g_{3} (v) + lo g_{3} (w)

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

What is log_{10}((x^8y^9)/(z^3)) ?
The solution to log_{10}((x^8y^9)/(z^3)) is 8log_{10}(x)+9log_{10}(y)-3log_{10}(z)