高一对数函数题 3^x=4^y=36 求2/x+1/y
问题描述:
高一对数函数题 3^x=4^y=36 求2/x+1/y
答
3^x=4^y=36 x=log3(36)=log3(4)+log3(9)=2log3(2)+2=2lg2/lg3+2y=log4(36)=lg36/lg4=1+lg3/lg22/x+1/y=1/(lg2/lg3+1)+1/(1+lg3/lg2)=lg3/(lg2+lg3)+lg2/(lg2+lg3)=(lg3+lg2)/(lg2+lg3)=1