(4) Solve the equation $\frac{1}{2}\left(a^{x}+a^{-x}\right)=m(a>0, a \neq 1)$.
(4) (1) When $m>1$, the original equation has two solutions
$x=\log _{a}\left(m \pm \sqrt{m^{2}-1}\right)$; (2) When $m<1$, the original equation has no solution; (3) When $m=1$, the original equation has the solution $x=0$