log9∧5=a,log3∧7=b,试用a,b表示log21∧35

问题描述:

log9∧5=a,log3∧7=b,试用a,b表示log21∧35

答:
a=log9(5)=log3(5)/log3(9)=log3(5) /2,log3(7)=b
所以:log3(5)=2a
log21(35)
=log3(35)/log3(21)
=[ log3(5)+log3(7) ]/ [log3(3)+log3(7) ]
=(2a+b) /(1+b)