log2(3)=a log3(7)=b 那么log14(56)=多少？要过程

log2(3)=a

3=2^a

log3(7)=b

7=3^b=(2^a)^b=2^(a×b)

log2(7)=a×b

log14(56)=log14(14×4)=log14(14)+log14(4)=1+2log14(2)=1+2[log2(2)]/[log2(14)]

=1+2/log2(14)=1+2/log2(2×7)=1+2/[log2(2)+log2(7)]=1+2/(1+a×b)

log2(3)=a

lg(2)=a*lg(3)

lg(7)=b*lg(3)

log14(56)=lg(56) / lg(14)=[ lg(7) +3 lg(2) ]/ [lg(2) +lg(7)]=[b*lg(3)+3 *a*lg(3) ]/ [a*lg(3) +b*lg(3)]=(b+3a)/(b+a)