Prove the following theorems: Theorem: Log2(11) is irrational **log base 2 of 11** Solution assume log2(11)=a/b where a and b are integers and a/b is reduced 2a/b=11 raise both side to b power 2a =11 b since 2 divides 2a , 2 must divide 11b Since 11 is prime, 2 does not divide 11 so 2 does not divide 11b this contradiction means our assumption was wrong and log2(11) cannot equal a rational a/b.

1. Prove the following theorems:
Theorem: Log2(11) is irrational
**log base 2 of 11**
Solution
assume log2(11)=a/b where a and b are integers and a/b is reduced
2a/b=11 raise both side to b power
2a =11 b since 2 divides 2a , 2 must divide 11b
Since 11 is prime, 2 does not divide 11 so 2 does not divide 11b
this contradiction means our assumption was wrong and log2(11) cannot equal a rational a/b