Solve $3^{2x}=9^{5x-2}$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$x=\frac{2}{3}$
Antwoord 2 correct
Fout
Antwoord 3 optie
There is no solution.
Antwoord 3 correct
Fout
Antwoord 4 optie
$x=2$
Antwoord 4 correct
Fout
Antwoord 1 optie
$x=\frac{1}{2}$.
Antwoord 1 feedback
Correct: $$\begin{align}
3^{2x}=9^{5x-2} & \Leftrightarrow 3^{2x}=(3^2)^{5x-2} \\
& \Leftrightarrow 3^{2x}=3^{2 \cdot(5x-2)} \\
& \Leftrightarrow 3^{2x}=3^{10x-4} \\
& \Leftrightarrow 2x=10x-4 \\
& \Leftrightarrow -8x=-4 \\
& \Leftrightarrow x=\frac{1}{2}. \\
\end{align}$$
Go on.
Antwoord 2 feedback
Wrong: $$\begin{align*}3^{2x}=9^{5x-2} & \not\Leftrightarrow 2x=5x-2\end{align*}$$
See Feature exponential functions.
Antwoord 3 feedback
Wrong: This equation can be solved.
See Properties exponential functions.
Antwoord 4 feedback
Wrong: $$\begin{align*}3^{2x}=9^{5x-2} & \not\Leftrightarrow 9^{4x}=9^{5x-2}\end{align*}$$
See Properties exponential functions.