log7 (56)
=log7 (7*8)
=log7 (7)+log7 (8)
=1+log7 (8)
=1+3*log7 (2)
=1+3ln(2)/ln(7)而由已知得到
a=log56 (14)
=ln(14)/ln(56)
=[ln(2)+ln(7)]/[ln(7)+3*ln(2)];解得
aln(7)+3aln(2)=ln(7)+ln(2);
ln(2)=ln(7)*(1-a)/(3a-1);
所以ln(2)/ln(7)=(1-a)/(3a-1);代入得到
log7 (56)=1+3ln(2)/ln(7)
=1+3(1-a)/(3a-1)
=[3a-1+3-3a]/(3a-1)
=2/(3a-1)