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})

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lo g_{5} (x) - 8 lo g_{5} (y) - 9 lo g_{5} (z)

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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))