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

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

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simplify log_{10}(x)+2log_{10}(y)-3log_{10}(x)y

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

lo g_{10} (\frac{y}{1000000})

- \frac{1}{5} lo g_{2} (\frac{1}{5}) - \frac{4}{5} lo g_{2} (\frac{4}{5})

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

8 lo g_{10} (a) + lo g_{10} (d)

ln (2 x^{3})

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