Question

Is log2 is rational or irrational. justify your answer

Answer 1

how to prove that the log 2 was irrational or rational :
Assume log 2 is rational . 10Log 2 = m / n , where m and n are integers
2 ^ { m / n } = 10 2 ^ m = 10 ^ n
 2 ^ m = 2 ^ n 5 ^ n
2 ^ { m - n } = 5 ^ n
Let k = m - n , k integers 2 ^ k = 5 ^ n Because of 2 and 5 are relatively prime , then there is no k and n that meet , then there is no value of m and n are meet. Contradiction. So , log 2 was irrational .