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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

lo g_{5} (3) + lo g_{5} (6)

lo g_{5} (3) + lo g_{5} (8)

lo g_{4} (\frac{x}{64})

lo g_{10} (\frac{d}{n})

ln (\frac{1}{4 k})

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