1:已知10^a=2,100^b=3,则1000^(2a—b/3)等于多少?2:已知a>0,b>0,且a^b=b^a,b=9a,则a等于多少?3:已知f(x)=e^x—e^-x,g(x)=e^x+e^-x,设f(x)f(y)=4,g(x)g(y)=8,求g(x+y)/g(x—y)的值
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![1:已知10^a=2,100^b=3,则1000^(2a—b/3)等于多少?2:已知a>0,b>0,且a^b=b^a,b=9a,则a等于多少?3:已知f(x)=e^x—e^-x,g(x)=e^x+e^-x,设f(x)f(y)=4,g(x)g(y)=8,求g(x+y)/g(x—y)的值](/uploads/image/z/1170763-43-3.jpg?t=1%EF%BC%9A%E5%B7%B2%E7%9F%A510%EF%BC%BEa%3D2%2C100%EF%BC%BEb%3D3%2C%E5%88%991000%EF%BC%BE%EF%BC%882a%E2%80%94b%2F3%EF%BC%89%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F2%EF%BC%9A%E5%B7%B2%E7%9F%A5a%3E0%2Cb%3E0%2C%E4%B8%94a%EF%BC%BEb%3Db%EF%BC%BEa%2Cb%3D9a%2C%E5%88%99a%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F3%3A%E5%B7%B2%E7%9F%A5f%28x%29%3De%EF%BC%BEx%E2%80%94e%EF%BC%BE-x%2Cg%28x%29%3De%EF%BC%BEx%2Be%EF%BC%BE-x%2C%E8%AE%BEf%28x%29f%28y%29%3D4%2Cg%28x%29g%28y%29%3D8%2C%E6%B1%82g%28x%2By%29%2Fg%28x%E2%80%94y%EF%BC%89%E7%9A%84%E5%80%BC)
1:已知10^a=2,100^b=3,则1000^(2a—b/3)等于多少?2:已知a>0,b>0,且a^b=b^a,b=9a,则a等于多少?3:已知f(x)=e^x—e^-x,g(x)=e^x+e^-x,设f(x)f(y)=4,g(x)g(y)=8,求g(x+y)/g(x—y)的值
1:已知10^a=2,100^b=3,则1000^(2a—b/3)等于多少?
2:已知a>0,b>0,且a^b=b^a,b=9a,则a等于多少?
3:已知f(x)=e^x—e^-x,g(x)=e^x+e^-x,设f(x)f(y)=4,g(x)g(y)=8,求g(x+y)/g(x—y)的值
1:已知10^a=2,100^b=3,则1000^(2a—b/3)等于多少?2:已知a>0,b>0,且a^b=b^a,b=9a,则a等于多少?3:已知f(x)=e^x—e^-x,g(x)=e^x+e^-x,设f(x)f(y)=4,g(x)g(y)=8,求g(x+y)/g(x—y)的值
1000^(2a—b/3)
=1000^2a/(1000^b)^1/3=
10^(3*2*a)/10^(3*b*1/3)
=(10^a)^6/10^b=2^6/3=64/3
a^b=a^(9a)=(a^a)^9
b^a=(9a)^a=9^a*a^a
所以a^8=9
a=9^(1/8)
f(x)f(y)=(e^x—e^-x)*(e^y—e^-y)
=e^(x+y)+e^-(x+y)-e^(x-y)—e^(y-x)
=g(x+y)-e^(x-y)—e^(y-x)=
=g(x+y)-g(x-y)=4
g(x+y)=(e^x+e^-x)*(e^y+e^-y)
=g(x+y)+g(x-y)=8
g(x+y)=6,g(x-y)=-2
g(x+y)/g(x—y)=6/(-2)=-3