Exercise 3 | Wiskunde op Tilburg University

Determine all

$x$ such that

$3\cdot \;^5\!\log (x)<\;^5\!\log (5x)+\;^5\!\log (60x) -(\;^5\!\log(3x)+2)$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$x<-2$ and

$0<x<2$

Antwoord 2 correct

Fout

Antwoord 3 optie

$x>0$

Antwoord 3 correct

Fout

Antwoord 4 optie

$x<-2$ and

$x>2$

Antwoord 4 correct

Fout

Antwoord 1 optie

$0<x<2$

Antwoord 1 feedback

Correct:

$\begin{align*} 3\cdot \;^5\!\log (x)=\;^5\!\log (5x)+\;^5\!\log (60x) -(\;^5\!\log(3x)+2)\\ \Leftrightarrow &\;^5\!\log (x^3)=\;^5\!\log (5x)+\;^5\!\log (60x) -\;^5\!\log(3x)-\;^5\!\log (25)\\ \Leftrightarrow &\;^5\!\log (x^3)=\;^5\!\log (\frac{5x\cdot 60x}{3x \cdot 25})\\ \Leftrightarrow & \;^5\!\log (x^3)=\;^5\!\log (4x)\\ \Leftrightarrow &x^3=4x\\ \Leftrightarrow &x^3-4x=0\\ \Leftrightarrow &x(x^2-4)=0\\ \Leftrightarrow & x=0 \mbox{ or } x=-2 \mbox{ or } x=2. \end{align*}$

$x=0$ and

$x=-2$ are outside the domain of the function. Hence,

$x=2$ . Via a sign chart we find

$0<x<2$ .

Go on.

Antwoord 2 feedback

Wrong: Consider the domain of a logarithmic function.

See Logarithmic functions.

Antwoord 3 feedback

Wrong: Calculate all the solutions of the corresponding equation.

See Properties logarithmic functions.

Antwoord 4 feedback

Wrong: Consider the domain of a logarithmic function.

See Logarithmic functions.