Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\log\left ( \sqrt{3+\sqrt 5}+\sqrt{3-\sqrt 5} \right )$ is gelijk aan (Briggse logaritmen)	A. 1
B.
C.
D.
E. 5

$https://latex.codecogs.com/png.image?\dpi{110}\log\left ( \sqrt{3+\sqrt 5}+\sqrt{3-\sqrt 5} \right )$ is equal to	A. 1
	B.
	C.
	D.
	E. 5

$\begin{aligned} \log\left(\sqrt{3+\sqrt 5}+\sqrt{3-\sqrt 5}\right)\\=\frac22\log\left(\sqrt{3+\sqrt5}+\sqrt{3-\sqrt5}\right)\\=\frac22\log\left(\sqrt{3+\sqrt5}+\sqrt{3-\sqrt5}\right)^2\\=\frac12\log\left(3+\sqrt5+\sqrt{3+\sqrt5}.\sqrt{3-\sqrt5}+3-\sqrt5\right)\\=\frac12\log\left(6+2.\sqrt{3+\sqrt5}.\sqrt{3-\sqrt5}\right)\\=\frac12\log\left(6+2.\sqrt{(3+\sqrt5)(3-\sqrt5)}\right)\\=\frac12\log(6+2\sqrt{9-5}=\frac12\log(6+2.2)=\frac12\log10=\frac12\end{aligned}$