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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

lo g_{b} (y^{5} x)

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

lo g_{5} (\frac{y}{125})

lo g_{10} (\frac{11 x ^{3} y}{z + 1})

lo g_{10} (\frac{27}{15 z})

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