Exercise 1 | Wiskunde op Tilburg University

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.