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

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

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

simplify

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

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

Solution steps

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

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

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

ln (\frac{( x ^{2} - 1 )}{x ^{9}})

7 lo g_{7} (5 x)

lo g_{10} (\frac{2 a ^{2}}{b})

lo g_{b} (\frac{3.839}{0.32})

lo g_{3} (\frac{z}{9})

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