Exercise 4 | Wiskunde op Tilburg University

Solve

$\textrm{ln}(4\cdot 2^{3x})+3\cdot \textrm{ln}(16) = \textrm{ln}(512\cdot 2^{x^2+3x+1})$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$x=2$

Antwoord 2 correct

Fout

Antwoord 3 optie

There is no solution.

Antwoord 3 correct

Fout

Antwoord 4 optie

$x=\sqrt{4088}$

Antwoord 4 correct

Fout

Antwoord 1 optie

None of the other answers is correct.

Antwoord 1 feedback

Correct:

$\begin{align*} \textrm{ln}(4\cdot 2^{3x})+3\cdot \textrm{ln}(16) = \textrm{ln}(512\cdot 2^{x^2+3x+1}) & \Leftrightarrow \textrm{ln}(4\cdot 2^{3x})+ \textrm{ln}(16^{3}) = \textrm{ln}(512\cdot 2^{x^2+3x+1})\\ & \Leftrightarrow \textrm{ln}(16^3\cdot 4\cdot 2^{3x}) = \textrm{ln}(512\cdot 2^{x^2+3x+1})\\ & \Leftrightarrow 16^3\cdot 4\cdot 2^{3x} = 512\cdot 2^{x^2+3x+1}\\ & \Leftrightarrow 2^{12}\cdot 2^2\cdot 2^{3x} = 2^9\cdot 2^{x^2+3x+1}\\ & \Leftrightarrow 2^{3x+14} = 2^{x^2+3x+10}\\ & \Leftrightarrow 3x+14 = x^2+3x+10\\ & \Leftrightarrow x^2-4 = 0\\ & \Leftrightarrow x=-2 \mbox{ or } x=2. \end{align*}$

Antwoord 2 feedback

Wrong: What are the solutions to

$x^2=4$ ?

Try again.

Antwoord 3 feedback

Wrong: First of all apply the Properties of logarithmic functions to get on both sides of the equation one ln-term.

See Properties logarithmic functions.

Antwoord 4 feedback

Wrong: First of all apply the Properties of logarithmic functions to get on both sides of the equation one ln-term.

See Properties logarithmic functions.