Determine all $x$ such that ln$(x+3)\geq 3$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$x\geq \textrm{ln}(3)-3$
Antwoord 2 correct
Fout
Antwoord 3 optie
$x\geq \frac{1}{3}e^3$
Antwoord 3 correct
Fout
Antwoord 4 optie
$x\geq 0$
Antwoord 4 correct
Fout
Antwoord 1 optie
$x\geq e^3-3$
Antwoord 1 feedback
Correct: $$\begin{align*}
\textrm{ln}(x+3)=3 &\Leftrightarrow \textrm{ln}(x+3)=\textrm{ln}(e^3)\\
&\Leftrightarrow x+3=e^3\\
&\Leftrightarrow x=e^3-3.
\end{align*}$$
Hence, $x\geq e^3-3$.
Go on.
\textrm{ln}(x+3)=3 &\Leftrightarrow \textrm{ln}(x+3)=\textrm{ln}(e^3)\\
&\Leftrightarrow x+3=e^3\\
&\Leftrightarrow x=e^3-3.
\end{align*}$$
Hence, $x\geq e^3-3$.
Go on.
Antwoord 2 feedback
Wrong: ln$(x+3)=3$ cannot be rewritten as $x+3=\textrm{ln}(3)$.
See Extra explanation: natural logarithm.
See Extra explanation: natural logarithm.
Antwoord 3 feedback
Wrong: What is the solution of $x+3=e^3$?
Try again.
Try again.
Antwoord 4 feedback