What is 2log_{10}(x)+3log_{10}(xy) ?

The solution to 2log_{10}(x)+3log_{10}(xy) is log_{10}(x^5y^3)

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simplify 2log_{10}(x)+3log_{10}(xy)

simplify

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

lo g_{10} (x^{5} y^{3})

Solution steps

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

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

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

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

Apply log rule:

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

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

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

Simplify

x^{2} (x y)^{3} : x^{5} y^{3}

= lo g_{10} (x^{5} y^{3})

ln (2 e^{4})

ln (\frac{e}{11})

ln (\frac{a - x}{a + x})

\frac{3}{2} ln (x^{6}) - \frac{3}{4} ln (x^{8})

lo g_{10} (9 x^{2})

What is 2log_{10}(x)+3log_{10}(xy) ?
The solution to 2log_{10}(x)+3log_{10}(xy) is log_{10}(x^5y^3)