What is log_{10}((x^2y^3)/z) ?

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

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simplify log_{10}((x^2y^3)/z)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

lo g_{10} (x^{2} y^{3}) : 2 lo g_{10} (x) + 3 lo g_{10} (y)

= 2 lo g_{10} (x) + 3 lo g_{10} (y) - lo g_{10} (z)

lo g_{a} (\frac{h k ^{5}}{m n ^{3}})

2 lo g_{2} (2 x)

ln (e^{3} y^{5})

lo g_{4} (12) + lo g_{4} (7)

lo g_{9} (\frac{y}{81})

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