lg3/lg2=a lg2/lg3=1/a
lg7/lg3=b
lg56/lg14
=lg(7×8)/lg(2×7)
=(lg7+lg8)/(lg2+lg7)
=(lg7+3lg2)/(lg2+lg7)
=[lg7/lg3+3lg2/lg3]/[lg2/lg3+lg7/lg3]
=(b+3/a)/(1/a+b)
=(ab+3)/(ab+1)