Answer to Question #217348 in Algebra for Collins

Question

Evaluate α given that α= [log(e²e^log2)/2]^1/2 .

Answer 1

$\alpha =[log(e^2e^{log2})/2]^{1/2}=[\frac{log(e^2 2)}{2}]^{1/2} = [\frac{log(e^2)+log 2)}{2}]^{1/2}$

$= [\frac{2+log 2)}{2}]^{1/2}=[1+\frac{1}{2}log 2]^{1/2}=\sqrt{1+log(\sqrt 2)}$