Exercise 3 | Wiskunde op Tilburg University

Solve

$3 \cdot 9^{2x}\cdot \frac{1}{3^x}=\frac{1}{2}\cdot(\frac{1}{9})^{4x}+\frac{1}{6}\cdot 3^{-8x+1}$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$x=-\frac{1}{3}$

Antwoord 2 correct

Fout

Antwoord 3 optie

$x=3$

Antwoord 3 correct

Fout

Antwoord 4 optie

$x=\frac{5}{7}$

Antwoord 4 correct

Fout

Antwoord 1 optie

$x=-\frac{1}{11}$

Antwoord 1 feedback

Correct:

$\begin{align*} 3 \cdot 9^{2x}\cdot \frac{1}{3^x}=\frac{1}{2}\cdot(\frac{1}{9})^{4x}+\frac{1}{6}\cdot 3^{-8x+1} & \Leftrightarrow 3^1 \cdot (3^2)^{2x}\cdot 3^{-x}=\frac{1}{2}\cdot(3^{-2})^{4x}+\frac{1}{6}\cdot 3^{-8x+1}\\ & \Leftrightarrow 3^1 \cdot 3^{4x} \cdot 3^{-x}=\frac{1}{2}\cdot 3^{-8x}+\frac{1}{6}\cdot 3^1 \cdot3^{-8x}\\ & \Leftrightarrow 3^{3x+1}=\frac{1}{2}\cdot3^{-8x}+\frac{3}{6} \cdot3^{-8x}\\ & \Leftrightarrow 3^{3x+1}=3^{-8x}\\ & \Leftrightarrow 3x+1=-8x\\ & \Leftrightarrow 11x =-1\\ & \Leftrightarrow x =-\frac{1}{11}. \end{align*}$

Go on.

Antwoord 2 feedback

Wrong:

$(3^2)^{2x} \neq 3^{2x+2}$ .

See Properties exponential functions.

Antwoord 3 feedback

Wrong: See Properties exponential functions.

Antwoord 4 feedback

Wrong: See Properties exponential functions.