Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

Wat is de oplossing van $https://latex.codecogs.com/png.image?\dpi{110}(\sqrt 2)^x\cdot(\sqrt 8)^x = \sqrt 4$	A. 1
B.
C.
D.
E.

What is the solution of $(\sqrt 2)^x\cdot(\sqrt 8)^x = \sqrt 4$	A. 1
B.
C.
D.
E.

1^ste manier :
$\begin{aligned} (\sqrt 2)^x\cdot(\sqrt 8)^x=\sqrt 4\;\Leftrightarrow(\sqrt 2)^x\cdot(2\sqrt2)^x=2\Leftrightarrow(\sqrt 2)^x\cdot2^x\cdot(2\sqrt2)^x=2\\\Leftrightarrow 2^x.2^x=2\Leftrightarrow 2^{2x}=2\Leftrightarrow 2x=1\Leftrightarrow x=\frac12 \end{aligned}$
2^de manier :
$\begin{aligned} (\sqrt 2)^x\cdot(\sqrt 8)^x=\sqrt 4\;\Leftrightarrow\;2^{\frac x2}.\left(2^{\frac32}\right)^x=2\;\Leftrightarrow\;2^{\frac{x+3x}{2}}=2\\\;\Leftrightarrow\;2^{\frac{4x}{2}}=2\;\Leftrightarrow\;2^{2x}=2\;\Leftrightarrow\;2x=1\;\Leftrightarrow\;x=\frac12 \end{aligned}$