Question

一条指数函数题已知3^x=4^y=36,求2/x+1/y的值,

Answer 1

∵3^x=4^y=36

∴x=log(3)36,y=log(4)36

∵log(3)36=lg36/lg3=1/(lg3/lg36)=1/log(36)3

同理log(4)36=1/log(36)4

（就是换底公式）

∴2/x+1/y=2/log(3)36+1/log(4)36

=2*log(36)3+log(36)4

=log(36)36

=1