Exercise 5 | Wiskunde op Tilburg University

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.

Antwoord 2 feedback

Wrong: ln

$(x+3)=3$ cannot be rewritten as

$x+3=\textrm{ln}(3)$ .

See Extra explanation: natural logarithm.

Antwoord 3 feedback

Wrong: What is the solution of

$x+3=e^3$ ?

Try again.

Antwoord 4 feedback

Wrong: You cannot just delete the logarithm.

See Logarithmic functions.