#### To determine

**To prove:**

log25 is an irrational number.

#### Answer

log25 is an irrational number.

#### Explanation

**Given:**

log25

**Formulae used:**

The logarithm property logmn=logenlogem

Let log25=pq for some non-zero integer *p* and *q*.

Therefore 5=2pq which will result in 2p=5q for some non-zero integers *p* and *q*.

By fundamental theorem of arithmetic, this is not possible.

Hence, log25 must be irrational.

**Conclusion:** Hence, the value of the expression log25 is an irrational number.