Answer and explanation:
To prove : [tex]\log_2 11[/tex] is irrational ?
Proof :
Let [tex]\log_2 11[/tex] is rational number.
So, It can be expressed in p/q form where, p and q are integers and q is non-zero.
[tex]\log_2 11=\frac{p}{q}[/tex]
Using property of logarithm,
[tex]11=(2)^{\frac{p}{q}}[/tex]
or [tex]11^q=(2)^{p}[/tex]
Which means 11 must be divisible by 2 for some p and q,
But 11 and 2 are co-prime.
So, Our assumption is not true.
[tex]\log_2 11[/tex] is irrational number.
Hence proved.
