What is log_{2}(6)-6log_{2}(x)+1/2 log_{2}(x+1) ?

The solution to log_{2}(6)-6log_{2}(x)+1/2 log_{2}(x+1) is log_{2}(6/(x^6))+(log_{2}(x+1))/2

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simplify log_{2}(6)-6log_{2}(x)+1/2 log_{2}(x+1)

simplify

lo g_{2} (6) - 6 lo g_{2} (x) + \frac{1}{2} lo g_{2} (x + 1)

lo g_{2} (\frac{6}{x ^{6}}) + \frac{lo g _{2} ( x + 1 )}{2}

Solution steps

lo g_{2} (6) - 6 lo g_{2} (x) + \frac{1}{2} lo g_{2} (x + 1)

- 6 lo g_{2} (x) = - lo g_{2} (x^{6})

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

= lo g_{2} (6) - lo g_{2} (x^{6}) + 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} (6) - lo g_{2} (x^{6}) = lo g_{2} (\frac{6}{x ^{6}})

= lo g_{2} (\frac{6}{x ^{6}}) + 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{6}{x ^{6}}) + \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{6}{x ^{6}}) + \frac{lo g _{2} ( x + 1 )}{2}

5 lo g_{4} (\frac{a ^{2} b}{n ^{3}})

lo g_{10} (a) + 8 lo g_{10} (b)

6 lo g_{10} (x) + 4 lo g_{10} (y)

ln (4 e^{2})

lo g_{b} (3) + lo g_{b} (5)

What is log_{2}(6)-6log_{2}(x)+1/2 log_{2}(x+1) ?
The solution to log_{2}(6)-6log_{2}(x)+1/2 log_{2}(x+1) is log_{2}(6/(x^6))+(log_{2}(x+1))/2