一条指数函数题已知3^x=4^y=36,求2/x+1/y的值,

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一条指数函数题已知3^x=4^y=36,求2/x+1/y的值,
一条指数函数题
已知3^x=4^y=36,求2/x+1/y的值,

一条指数函数题已知3^x=4^y=36,求2/x+1/y的值,
∵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

x=log3(36)=1g36/lg3
y=log4(36)=1g36/lg4
2/x+1/y=2lg3/lg36 + lg4/lg36 = (2lg3+lg4)/lg36= lg(3*3*4)/lg36=lg36/lg36=1

3^x=4^y=36
所以x=log3底36 y=log4底36
2/x+1/y=log36底9+log36底4=1

3^x=4^y=36
x=以3为低的log36=lg36/lg3,y=以4为低的log36=lg36/lg4
2/x+1/y=2/lg36/lg3+1/lg36/lg4
=(2lg3+lg4)/lg36
=(lg9+lg4)/lg36
=lg36/lg36
=1