Exercise 1 | Wiskunde op Tilburg University

Determine

$p$ such that

$2\cdot \;^3\!\log (5) - \;^3\!\log (10) + \;^3\!\log (4) + \;^3\!\log (1) = \;^3\!\log (p)$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$p=20$

Antwoord 2 correct

Fout

Antwoord 3 optie

$p=4$

Antwoord 3 correct

Fout

Antwoord 4 optie

$p=0$

Antwoord 4 correct

Fout

Antwoord 1 optie

$p=10$

Antwoord 1 feedback

Correct:

$\begin{align*} 2\cdot \;^3\!\log (5) - \;^3\!\log (10) + \;^3\!\log (4) + \;^3\!\log (1) & = \;^3\!\log (5^2) - \;^3\!\log (10) + \;^3\!\log (4) + \;^3\!\log (1)\\ & = \;^3\!\log (25) - \;^3\!\log (10) + \;^3\!\log (4) + \;^3\!\log (1)\\ & = \;^3\!\log (\frac{25 \cdot 4 \cdot 1}{10})\\ & = \;^3\!\log (10).\\ \end{align*}$

Hence,

$p=10$ .

Go on.

Antwoord 2 feedback

Wrong:

$\;^3\!\log (25) - \;^3\!\log (10) + \;^3\!\log (4) + \;^3\!\log (1) \neq \;^3\!\log (25-10+4+1)$ .

See Properties logarithmic functions.

Antwoord 3 feedback

Wrong:

$2\cdot \;^3\!\log (5) \neq \;^3\!\log (2\cdot 5)$ .

See Properties logarithmic functions.

Antwoord 4 feedback

Wrong:

$\;^3\!\log (25) - \;^3\!\log (10) + \;^3\!\log (4) + \;^3\!\log (1) \neq \;^3\!\log (\frac{10\cdot 4 \cdot 0}{10})$ .

See Properties logarithmic functions.