3^x=4^y=36,则2/x+1/y等于多少?

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3^x=4^y=36,则2/x+1/y等于多少?
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3^x=4^y=36,则2/x+1/y等于多少?
3^x=4^y=36,则2/x+1/y等于多少?

3^x=4^y=36,则2/x+1/y等于多少?
∵3^x=4^y=36
∴x=log(3)(36)
y=log(4)(36)
∴2/x+1/y
=2/log(3)(36) + 1/log(4)(36)
根据换底公式 可知1/log(3)(36)=log(36)(3)
同理1/log(4)(36)=log(36)(4)
∴2/x+1/y=2*log(36)(3)+log(36)(4)
=log(36)(9)+log(36)(4)
=log(36)(36)
=1.

3^x=xLn(3)
4^y=yLn(4)
2/x+1/y = (2ln3 +ln4)/36

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

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