Exercise 2 | Wiskunde op Tilburg University

Rewrite the following expression as one logarithm:

$\textrm{log}(2x)+3\cdot\textrm{log}(y)-\textrm{log}(\frac{1}{y})-\textrm{log}(z^2)$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

log

$(\dfrac{6x}{z^2})$

Antwoord 2 correct

Fout

Antwoord 3 optie

log

$(2x+y^3-\dfrac{1}{y}-z^2)$

Antwoord 3 correct

Fout

Antwoord 4 optie

log

$(\dfrac{2xy^2}{z^2})$

Antwoord 4 correct

Fout

Antwoord 1 optie

log

$(\dfrac{2xy^4}{z^2})$

Antwoord 1 feedback

Correct:

$\begin{align*} \textrm{log}(2x)+3\cdot\textrm{log}(y)-\textrm{log}(\frac{1}{y})-\textrm{log}(z^2) & = \textrm{log}(2x)+\textrm{log}(y^3)-\textrm{log}(\frac{1}{y})-\textrm{log}(z^2)\\ & = \textrm{log}(2x)+\textrm{log}(y^3)+\textrm{log}(y)-\textrm{log}(z^2)\\ &= \textrm{log}(\frac{2xy^4}{z^2}) \end{align*}$

Go on.

Antwoord 2 feedback

Wrong:

$\textrm{log}(2x)+\textrm{log}(y^3)-\textrm{log}(\frac{1}{y})-\textrm{log}(z^2) \neq \textrm{log}(2x+y^3-\frac{1}{y}-z^2)$ .

See Properties logarithmic functions.

Antwoord 3 feedback

Wrong:

$3\cdot \textrm{log}(y) \neq \textrm{log}(3y)$ .

See Properties logarithmic functions.

Antwoord 4 feedback

Wrong:

$-\textrm{log}(\frac{1}{y}) = \textrm{log}(y)$ .

See Properties logarithmic functions.