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

The solution to 2log_{2}(x)-log_{2}(x-3) is log_{2}((x^2)/(x-3))

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simplify 2log_{2}(x)-log_{2}(x-3)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{2} (x^{2}) - lo g_{2} (x - 3) = lo g_{2} (\frac{x ^{2}}{x - 3})

= lo g_{2} (\frac{x ^{2}}{x - 3})

ln (5 e^{2 x})

ln (\frac{100}{50})

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

ln^{3} (a b^{2})

ln (\frac{a + 1}{a})

What is 2log_{2}(x)-log_{2}(x-3) ?
The solution to 2log_{2}(x)-log_{2}(x-3) is log_{2}((x^2)/(x-3))