帮忙做道题sinh[(ln(x)/6+sinh^(-1)(2/3)-ln(3000)/6]

Question

帮忙做道题sinh[(ln(x)/6+sinh^(-1)(2/3)-ln(3000)/6]

Answer 1

sinhx =(e^x-e^-x)/2
e^(a+b+c)=e^a * e^b * e^c------------(0)
y=e^(lnx / 6)
lny= lnx/6=ln(x^(1/6))
y=x^(1/6)------------------------(1)
z=e^(-lnx / 6)
lnz= -lnx/6=-ln(x^(1/6))
z=1/(x^(1/6)) -------------------(2)
设x=3000,从 (2),
w=e^(-ln3000)/6=1/(3000^(1/6)-------------(3)
从 (1)
v= e^(ln3000)/6=3000^(1/6)----------------(4)
1/sinh(2/3)=2/(e^(2/3)-e^(-2/3))= u=常数
sinh u=(e^u-e^(-u))/2----------------------(5)
从(0)到(5)可以得到答案