Given the logarithm expression :

log2 (32)

We need to find the value.

We will assume that the value of log2 (32) = x

Now we will rewrite the equation using the exponent form.

==> log2 (32) = x

==> 2^x = 32

Now we will factor 32.

==> 32 = 2*2*2*2*2 = 2^5

==> 2^x = 2^5

Now we notice that the bases are the same, then the powers should be equal.

==> x = 5

**Then the exact value of log2 (32) = 5**

We have to find the value of log (2) 32.

Here the base of the log is 2.

We can write 32 as 2^5.

Now for any base log a^b = b*log a and log ( a) a = 1.

So log (2) 32

=> log (2) 2^5

=> 5* log (2) 2

=> 5

**Therefore log (2) 32 = 5**

We know that if a^y = x, then log(a) = y.

Now let log 2 32 = y.

Then 2^y = 32.

But 2^5 = 32.

So y =5.

Therefore log(2) 32 = 5.

**Therefore y = 5**, as 2^5 = 32.