What is log_{10}(xy)-1.7log_{10}(y^2) ?

The solution to log_{10}(xy)-1.7log_{10}(y^2) is log_{10}(x)-2.4log_{10}(y)

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simplify log_{10}(xy)-1.7log_{10}(y^2)

simplify

lo g_{10} (x y) - 1.7 lo g_{10} (y^{2})

lo g_{10} (x) - 2.4 lo g_{10} (y)

Solution steps

lo g_{10} (x y) - 1.7 lo g_{10} (y^{2})

Simplify

1.7 lo g_{10} (y^{2}) : 3.4 lo g_{10} (y)

= lo g_{10} (x y) - 3.4 lo g_{10} (y)

Apply log rule:

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

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

= (lo g_{10} (x) + lo g_{10} (y)) - 3.4 lo g_{10} (y)

Apply rule:

(a) = a

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

= lo g_{10} (x) + lo g_{10} (y) - 3.4 lo g_{10} (y)

Add similar elements:

lo g_{10} (y) - 3.4 lo g_{10} (y) = - 2.4 lo g_{10} (y)

= lo g_{10} (x) - 2.4 lo g_{10} (y)

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What is log_{10}(xy)-1.7log_{10}(y^2) ?
The solution to log_{10}(xy)-1.7log_{10}(y^2) is log_{10}(x)-2.4log_{10}(y)