对数函数已知log3`10=a,log6`25=b,求log4`45.

Question

对数函数
已知log3`10=a,log6`25=b,求log4`45.

Answer 1

log6`25=b
→log3`25/log3`6=b
→2log`5/(1+log3`2)=b.(1)
又由log3`10=a,得：
log3`5+log3`2=a.(2)
解(1)(2),得：log3`2=(2a+b)/(b+2),log3`5=(ab+b)/(b+2).
∴log4`45=log3`45/log3`4
=(2+log3`5)/2log3`2
=[2+(ab+b)/(b+2)]/[2(2a+b)/(b+2)]
=(ab+3b+4)/(4a+2b).