log2 3=a,log3 5=b,试用a,b 表示log30 45
问题描述：
log2 3=a,log3 5=b,试用a,b 表示log30 45
答
log2 3=a,log3 5=b,∴ log3 2=1/a∴ log30 45=log3(45)/log3(30)∵ log3(45)=log3(3²*5)=log3(3²)+log3(5)=2+blog3(30)=log3(2*3*5)=log3(2)+log3(3)+log3(5)=1/a+1+b=(1+a+ab)/a∴ log30 45=log3(45)/log...