对数函数代换

利用换底公式
log3,10=lg10/lg3=1/lg3=a,log6,25=lg25/lg6=2lg5/[lg2+lg3]=2(1-lg2)/[lg2+lg3]=b,
可推出lg3=1/a,lg2=2a-b/2(2+b),

故log4 45=lg45/lg4=[2lg3+1-lg2]/2lg2将上式代入即可!

log3 10=a
lg10/lg3=a
1/lg3=a
lg3=1/a

log6 25=b
lg25/lg6=b
lg(100/4)/(lg2+lg3)=b
(lg100-lg4)/(lg2+lg3)=b
(2-2lg2)/(lg2+lg3)=b
(2-2lg2)/(lg2+1/a)=b
2-2lg2=blg2+b/a
(b+2)lg2=2-b/a=(2a-b)/a
lg2=(2a-b)/a(b+2)

log4 45
=lg45/lg4
=(lg5+lg9)/2lg2
=(1-lg2+2lg3)/2lg2
=1/(2lg2)-1/2+lg3/lg2
=1/[2(2a-b)/a(b+2)]-1/2+(1/a)/[(2a-b)/a(b+2)]
=(ab+3b+4)/(4a-2b)