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.
\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.
See Properties logarithmic functions.
Antwoord 3 feedback
Antwoord 4 feedback