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

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

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

simplify

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

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

Solution steps

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

Cancel

\frac{x ^{2} x + 1}{x ^{3}} : \frac{x + 1}{x}

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

Apply log rule:

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

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

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

lo g_{10} (x y^{4})

lo g_{5} (7) + lo g_{5} (3)

\frac{1}{7} (lo g_{10} (x) - lo g_{10} (x + 4))

lo g_{10} (x + 3) + lo g_{10} (x)

ln (x^{5} (1 - x)^{3})

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