32 to the power of n = 2. n = ?

32^n = 2
(2^5)^n = 2
2^(5n) = 2^1
5n = 1
n = 1/5 (0.2)

2^5 = 32 so 32^(1/5) = 2 so n = 1/5

32=2^5
(2^5)^n=2
2^(5n)=2 so
5n=1
n=1/5

32^n=2
(2)^5n=(2)^1
since bases are same powers are equal
therefore,
5n=1
n=1/5