What is log_{2}(3)-3log_{2}(x)+1/2 log_{2}(x+1) ?

The solution to log_{2}(3)-3log_{2}(x)+1/2 log_{2}(x+1) is log_{2}(3/(x^3))+(log_{2}(x+1))/2

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simplify log_{2}(3)-3log_{2}(x)+1/2 log_{2}(x+1)

simplify

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

lo g_{2} (\frac{3}{x ^{3}}) + \frac{lo g _{2} ( x + 1 )}{2}

Solution steps

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

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

\frac{1}{2} lo g_{2} (x + 1) = lo g_{2} ((x + 1)^{\frac{1}{2}})

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

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

= lo g_{2} (\frac{3}{x ^{3}}) + lo g_{2} ((x + 1)^{\frac{1}{2}})

Simplify

lo g_{2} ((x + 1)^{\frac{1}{2}}) : \frac{1}{2} lo g_{2} (x + 1)

= lo g_{2} (\frac{3}{x ^{3}}) + \frac{1}{2} lo g_{2} (x + 1)

Simplify

\frac{1}{2} lo g_{2} (x + 1) : \frac{lo g _{2} ( x + 1 )}{2}

= lo g_{2} (\frac{3}{x ^{3}}) + \frac{lo g _{2} ( x + 1 )}{2}

ln (\frac{x + y}{x - y})

2 [3 ln (x) - ln (x + 1) - ln (x - 1)]

- lo g_{b} (\frac{1}{2})

ln (x^{2} y^{5})

lo g_{x} (x x)

What is log_{2}(3)-3log_{2}(x)+1/2 log_{2}(x+1) ?
The solution to log_{2}(3)-3log_{2}(x)+1/2 log_{2}(x+1) is log_{2}(3/(x^3))+(log_{2}(x+1))/2