Wiskunde Multiple Choice Vraag

$\ln(\sqrt2+\sqrt6)+\ln(\sqrt3-1)=$	A. $\frac12\ln 2$
	B. $\frac32\ln 2$
	C. $\frac12\ln 3$
	D. $\frac32\ln 3$
	E. $\ln 2 + \ln 3$

[ 6-8351 - op net sinds 28.6.2025-(E)-26.8.2025 ]

Translation in E N G L I S H

IN CONSTRUCTION

Oplossing - Solution

$\begin{aligned}&\ln(\sqrt2+\sqrt6)+\ln(\sqrt3-1)\\&=\ln\left(\sqrt2(1+\sqrt3)\right)+\ln(\sqrt3-1)\\&=\ln\sqrt2+\ln(1+\sqrt3)+\ln(\sqrt3-1)\\&=\ln\sqrt2+\ln\left((\sqrt3)^2-1^2\right)\\&=\frac12\ln2+\ln2\\&=\frac32\ln2\end{aligned}$

$\ln(\sqrt2+\sqrt6)+\ln(\sqrt3-1)=$	A. \(\frac12\ln 2\)
	B. \(\frac32\ln 2\)
	C. \(\frac12\ln 3\)
	D. \(\frac32\ln 3\)
	E. \(\ln 2 + \ln 3\)