Jeśli log3 z 2 = a, oraz log3 z 5 = b, wtedy liczba log3 z 200 jest rowna:
A. 3a+2b
B. 32ab
C. 2a + 3b
D. 3a +b
A. 3a+2b
B. 32ab
C. 2a + 3b
D. 3a +b
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Odpowiedź:
[tex]log_3 200 = log_3 ( 25*8) = log_3 25 + log_3 8 = log_3 5^2 + log_3 2^3 =\\= 2 log_3 5 + 3 log_3 2 = 2 b + 3 a = 3 a + 2 b[/tex]
Szczegółowe wyjaśnienie: