What is sqrt(2)^{log_{2}(n)} ?

The solution to sqrt(2)^{log_{2}(n)} is 2^{(log_{2}(n))/2}

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simplify sqrt(2)^{log_{2}(n)}

simplify

2^{l o g_{2} (n)}

2^{\frac{l o g _{2} ( n )}{2}}

Solution steps

(2)^{l o g_{2} (n)}

Apply radical rule:

a = a^{\frac{1}{2}}

= (2^{\frac{1}{2}})^{l o g_{2} (n)}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 2^{\frac{1}{2} l o g_{2} (n)}

Simplify

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

= 2^{\frac{l o g _{2} ( n )}{2}}

cos (a t) \cdot e^{- 2 t}

(\frac{50}{1.092 \cdot 1 0 ^{- 2}}) \cdot 1 0^{- 6}

\frac{sec ^{2} ( x ) - 1}{1 - cos ^{2} ( x )}

50000 (1.0152)^{- 4}

5000 \cdot \frac{e ^{0.22}}{e ^{0.08}}

What is sqrt(2)^{log_{2}(n)} ?
The solution to sqrt(2)^{log_{2}(n)} is 2^{(log_{2}(n))/2}