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

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

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simplify 2log_{a}(x)-log_{a}(y)

simplify

2 lo g_{a} (x) - lo g_{a} (y)

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

Solution steps

2 lo g_{a} (x) - lo g_{a} (y)

Apply log rule:

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

2 lo g_{a} (x) = lo g_{a} (x^{2})

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

Apply log rule:

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

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

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

\frac{2}{3} ln (\frac{A}{e})

2 lo g_{3} (x) - lo g_{3} (x - 2)

2 ln (a) - 5 ln (b) + ln (c)

ln (10 e^{- x})

ln (\frac{x ^{2} ( x + 1 )}{x + 2})

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