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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

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

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

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

lo g_{10} (y^{2}) = 2 lo g_{10} (y)

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

lo g_{2} ((3 x)^{3})

lo g_{6} (7 x^{2})

lo g_{4} (\frac{x ^{2} - 2 x - 3}{x ^{2} - 3 x})

ln (x^{8} y^{3} z)

ln (y \frac{y}{5 - y})

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