log(a)(e^x+e^-x+2)+log(a)(e^x+e^-x-2)

问题描述:

log(a)(e^x+e^-x+2)+log(a)(e^x+e^-x-2)

log(a)(e^x+e^-x+2)+log(a)(e^x+e^-x-2)
=log(a)[(e^x+e^-x+2)(e^x+e^-x-2)]
=log(a)[(e^x+e^-x)^2 - 4]
=log(a)[e^2x + 2 + e^-2x -4]
=log(a)[e^2x - 2 + e^-2x]
=log(a)[(e^x - e^-x)^2]
=2log(a)(e^x - e^-x)