(1) ln e^(-2x) = 8
(2) log_5 (625) = x
lne^a=a lne
now we may prove lne=1 so that you may get
lne^a =a lne = a
well lne is actually ln_e(e)
let ln_e(e)=t
then e^t=e
comparing both sides we get t=1
so ln_e(e)=lne=1 so
lne^a=a lne =a hence proved
1) lne^(-2x)=8
-2xlne=8
but lne=1 (already proved)
-2x=8
x=-4