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
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