Question

Wiedząc że :

log12=a i log2=b oblicz log90

Answer 1

log 12 = a  i log 2 = b

a = log 12 = log (3 · 4) = log 3 + log 4 = log 3 + log 2² = log 3 + 2·log 2 = log 3 + 2·b

Zatem:

a = log 3 + 2·b
log 3 = a - 2b

log 90 = log (10 · 9) = log 10 + log 9 = 1 + log 3² = 1 + 2·log 3 = 1 + 2·(a - 2b) = 1 + 2a - 4b
log 90 = 1 + 2a - 4b