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

The solution to log_{10}(x^2)-log_{10}(y)-log_{10}(x) is log_{10}(x/y)

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

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

Simplify

\frac{\frac{x ^{2}}{y}}{x} : \frac{x}{y}

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

lo g_{10} (\frac{2}{ab})

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

lo g_{7} (2401 x)

\frac{1}{2} lo g_{2} (5) - 2 lo g_{2} (7)

lo g_{3} (81 x)

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