Solution
= Solution
If $\log_2 3=a/b$ were a <rational number>, choose positive <integers> $a,b$ because $\log_2 3>0$. Exponentiation gives $2^a=3^b$, but the left side is even and the right side is odd. Thus
$$
\boxed{\log_2 3
otin\mathbb Q.}
$$
This is the basic <irrational logarithm criterion>: a rational logarithm would <force> positive <integer> powers of its base and argument to coincide.