# Rational numbers raised to an irrational power.

Rational numbers raised to an irrational power.
You can still ask an expert for help

## Want to know more about Irrational numbers?

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

${2}^{{\mathrm{log}}_{2}3}=3$ is rational.
Check that ${\mathrm{log}}_{2}3$ is irrational.
Suppose it is rational.
${\mathrm{log}}_{2}3=\frac{a}{b}$
where $gcd\left(a,b\right)=1$.
${3}^{b}={2}^{a}$which is a contradition.