Loesung zum Logarithmus

Ausführliche Lösungen

1. Finde die Basis
• Die Basis ist 16
log_x 256 = 2
256 = x² | √
x = 16
• Die Basis ist 6
log_x 216 = 3
216 = x³ | ³√
x = 6
• Die Basis ist 7
log_x 343 = 3
343 = x³ | ³√
x = 7
• Die Basis ist 14
log_x 196 = 2
196 = x² | √
x = 14
2. Finde die Zahl
• log₁₉ x = 2
x = 19² ==> x = 361
• log₁₈ x = 3
x = 18³ ==> x = 5832
• log₂₂ x = 2
x = 22² ==> x = 484
3. Berechne
• log₂ 32 = x
log(32) / log(2) = x ==> x = 5
• log₄ 4 = x
log(4) / log(4) = x ==> x = 1
• log₆ 36 = x
log(36) / log(6) = x ==> x = 2
• log₂ 64 = x
log(64) / log(2) = x ==> x = 6


4. Berechne nach x
• log_x 27 = 3
27 = x³ | ³√
x = 3
• log_x 25 = 2
25 = x² | √
x = 5