Question

log以3为底10的对数=a,log以6为底25的对数=b,求log以4为底45的对数=?

Answer 1

log3(10)=a,log3(2)+log3(5)=a,

log3(25)/log3(6)=b,[2log3(5)]/[log3(2)+1]=b,

log3(2)=(a-b)/(b+1),

log3(5)=[b(a+1)]/(b+1).

log4(45)=[log3(5)+2]/[2log3(2)]=[b(a+1)+2(b+1)]/[2(a-b)]=[ba+3b+2]/[2(a-b)].