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2009-10-17T17:59:18+02:00
Log5 4=a i log5 3=b, oblicz log25 12
log25 12 = log5 12/log5 25 = log5 (4*3)/2 = (log5 4 + log5 3)/2 = (a + b)/2

log3 4=a i log3 5=b, oblicz log27 0,8
log27 0,8 = log3 0,8/log3 27 = log3 (4/5)/3 = (log3 4 - log3 5)/3 = (a - b)/3

log14 2=a i log14 5 =b, oblicz log7 50
log14 2 = log7 2/log7 14 = log7 2/(log7 2 + 1) = a
log7 2 = a/(1 - a)
log14 5 = log7 5/log7 14 = log7 5/(log7 2 + 1) = log7 5/(a/(1 - a) + 1) = log7 5/[1/(1 - a)] = b
log7 5 = b/(1 - a)
log7 50 = log7 50 = 2log7 5 + log7 2 = a/(1 - a) + 2b/(1 - a) = (a + 2b/(1 - a)

log3 20=a i log3 15=b, oblicz log2 360
log3 20 = 2log3 2 + log3 5 = a
log3 15 = log3 3 + log3 5 = 1 + log3 5 = b
log3 5 = b - 1
log3 2 = (a - b + 1)/2
log2 360 = log3 360/log3 2 = log3 (20*9*2)/log3 2 = (log3 20 + log3 9 + log3 2)/log3 2 = [a + 2 + (a - b + 1)/2]/[(a - b + 1)/2] = [(3a - b + 5)/2]/[(a - b + 1)/2] = (3a - b + 5)/(a - b + 1)
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