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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

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

\frac{7}{2} ln (\frac{7}{2})

lo g_{10} (\frac{x y}{10})

5 ln (x) - \frac{1}{3} ln (y)

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

lo g_{x} (9) - lo g_{x} (15) + lo g_{x} (7)

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