已知2x=log2 3,求(2^3x-2^-3x)/(2^x-2^-x)的值
1个回答

月紫希希,

2X=log2(3)

X=1/2log2(3)

2^x=2^log2(√3)

2^x=√3

2^(3*x)-2^(-3x)/(2^x-2^-x)

=(2^x-2^(-x))(2^2x+1+2^(-2x))/(2^x-2^(-x))(2^x+2^(-x))

=(2^2x+1+2^(-2x))/(2^x+2^(-x))

=((2^x+2^(-x))^2-1)/(2^x+2^(-x))

=(2^x+2^(-x))-1/(2^x+2^(-x))

=(√3+1/√3)-1/(√3+1/√3)

=(3+1/√3)-(1/(3+1)/√3)

=4/√3-(√3/4)

=4√3/3-(√3/4)

=13√3/12