If a=b^c and b=c^a and c=a^b
show that abc=1

you don show us say abc=1.
wetin i wan show again

take log of both sides in each equation.....
log a = c log b...........1
log b = a log c............2
log c = b log a............3
subs 1 into 3
log c = b (c log b)
log c = bc log b..........4
subs 2 into 4
log c = bc (a log c)
log c = abc logc
log c / log c = abc
abc = 1
that's it

Beautiful @haryourdayG