найти log15 75, если log2 5=a, log2 3=b

Question

найти log15 75, если log2 5=a, log2 3=b

Answer 1

log15 75=(log2 75)/(log2 15)=(log2 (3*25)/(log2 (3*5)=(log2 3+log2 5^2)/(log2 3+log2 5)=(log2 3

+2log2 5)/(log2 3+log2 5)=(b+2a)/(b+a)