Fonctions exponentielles et logarithmes - Partie 1

Fonctions exponentielles et logarithmes - Partie 1#

Nom, prénom:

Note:

Question 1 2 Total
Points 3 3 6
Obtenus

Détails des calculs obligatoires. Attention au soin.
Réponse sous forme de valeur exacte simplifiée.
Calculatrice non autorisée.

Question 1 (3 pts)#

Calculez:

  1. \(64^{-\frac{1}{3}} = \)

  2. \(\log(10) = \)

  3. \(\log_3(27) = \)

  4. \(\log_2(\sqrt{2}) = \)

  5. \(\log(\dfrac{1}{1000}) = \)

  6. \(4^{\log_4(5)} = \)

Solution

  1. \(64^{-\frac{1}{3}} = \dfrac{1}{4}\)

  2. \(\log(10) = 1\)

  3. \(\log_3(27) = 3\)

  4. \(\log_2(\sqrt{2}) = \dfrac{1}{2}\)

  5. \(\log(\dfrac{1}{1000}) = -3\)

  6. \(4^{\log_4(5)} = 5\)

Question 2 (3 pts)#

Que vaut x ?

  1. \(5^x = 125 \qquad x = \)

  2. \(4^x = \dfrac{1}{16} \qquad x = \)

  3. \(7^{3x} = 7^{6} \qquad x = \)

  4. \(\log(x) = 4 \qquad x = \)

  5. \(\log_x(49) = 2 \qquad x = \)

  6. \(\log_3(x) = 0 \qquad x = \)

Solution

  1. \(5^x = 125 \qquad x = 3\)

  2. \(4^x = \dfrac{1}{16} \qquad x = -2\)

  3. \(7^{3x} = 7^{6} \qquad x = 2\)

  4. \(\log(x) = 4 \qquad x = 10\,000\)

  5. \(\log_x(49) = 2 \qquad x = 7\)

  6. \(\log_3(x) = 0 \qquad x = 1\)

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