What is log_{6}(x^2)-log_{6}(x)-log_{6}(y) ?

The solution to log_{6}(x^2)-log_{6}(x)-log_{6}(y) is log_{6}(x/y)

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simplify log_{6}(x^2)-log_{6}(x)-log_{6}(y)

simplify

lo g_{6} (x^{2}) - lo g_{6} (x) - lo g_{6} (y)

lo g_{6} (\frac{x}{y})

Solution steps

lo g_{6} (x^{2}) - lo g_{6} (x) - lo g_{6} (y)

Apply log rule:

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

lo g_{6} (x^{2}) - lo g_{6} (x) = lo g_{6} (\frac{x ^{2}}{x})

= lo g_{6} (\frac{x ^{2}}{x}) - lo g_{6} (y)

Cancel the common factor:

x

= lo g_{6} (x) - lo g_{6} (y)

Apply log rule:

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

lo g_{6} (x) - lo g_{6} (y) = lo g_{6} (\frac{x}{y})

= lo g_{6} (\frac{x}{y})

lo g_{10} (8) - 2 lo g_{10} (6) - lo g_{10} (3)

ln (\frac{4}{4 + 2})

lo g_{8} (\frac{z}{64})

lo g_{5} (4 x^{7})

lo g_{2} (\frac{3}{2 x})

What is log_{6}(x^2)-log_{6}(x)-log_{6}(y) ?
The solution to log_{6}(x^2)-log_{6}(x)-log_{6}(y) is log_{6}(x/y)