以12为底6的对数为a,则有
a=lg6/lg12=(lg2+lg3)/(2lg2+lg3)
整理得lg2/lg3=(1-a)/(2a-1)
24为底的18的对数
=lg18/lg24
=(2lg3+lg2)/(3lg2+lg3)
=(2+lg2/lg3)/(3lg2/lg3+1)
=[2+(1-a)/(2a-1)]/[1+3(1-a)/(2a-1)]
=[(4a-2+1-a)/(2a-1)]/[(2a-1+3-3a)/(2a-1)]
=(3a-1)/(2-a)