Question

(a) 32^x=32
(b) 5^x-3=1/25

Answer 1

Anything raised to the power gives the same number.
so  in the first case x is 32.

We know that 5 raised to the power (-2) is 1/25
hence x-3=(-2) and x=1

Answer 2

a.
32^x = 32
or log (32^x) = log 32
or x log 32 = log 32
(divide both sides by log 32)
or x = 1.

b.
5^(x-3) = 1/25
or log (5^(x-3)) = log (1/25)
or log (5^(x-3)) = log (5^(-2))
or (x-3) log (5) = -2 log (5)
(divide both sides by log 5)
or x-3 = -2
or x = -2+3
or x = 1