What is 3log_{2}(x)-(log_{2}(3)-log_{2}(x+4)) ?

The solution to 3log_{2}(x)-(log_{2}(3)-log_{2}(x+4)) is log_{2}((x^3(x+4))/3)

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simplify 3log_{2}(x)-(log_{2}(3)-log_{2}(x+4))

simplify

3 lo g_{2} (x) - (lo g_{2} (3) - lo g_{2} (x + 4))

lo g_{2} (\frac{x ^{3} ( x + 4 )}{3})

Solution steps

3 lo g_{2} (x) - (lo g_{2} (3) - lo g_{2} (x + 4))

Apply log rule:

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

lo g_{2} (3) - lo g_{2} (x + 4) = lo g_{2} (\frac{3}{x + 4})

= 3 lo g_{2} (x) - lo g_{2} (\frac{3}{x + 4})

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

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

= lo g_{2} (x^{3}) - lo g_{2} (\frac{3}{x + 4})

Apply log rule:

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

lo g_{2} (x^{3}) - lo g_{2} (\frac{3}{x + 4}) = lo g_{2} (\frac{x ^{3}}{\frac{3}{x + 4}})

= lo g_{2} (\frac{x ^{3}}{\frac{3}{x + 4}})

Simplify

\frac{x ^{3}}{\frac{3}{x + 4}} : \frac{x ^{3} ( x + 4 )}{3}

= lo g_{2} (\frac{x ^{3} ( x + 4 )}{3})

lo g_{3} (x + 1) - lo g_{3} (x^{2} - 1)

lo g_{5} (10 x)

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

4 lo g_{b} (x) + 5 lo g_{b} (z)

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

What is 3log_{2}(x)-(log_{2}(3)-log_{2}(x+4)) ?
The solution to 3log_{2}(x)-(log_{2}(3)-log_{2}(x+4)) is log_{2}((x^3(x+4))/3)