Question

The value of $3^{\sqrt{{\log }_{3}4}}$ is equal to

• A. $3^{\sqrt{{\log }_{4}3}}$
• B. $4^{\sqrt{{\log }_{4}3}}$
• C. $4^{\sqrt{{\log }_{3}4}}$
• D. $0$

Answer 1

The correct option is B $4^{\sqrt{{\log }_{4}3}}$

$3^{\sqrt{{\log }_{3}4}}=3^{\frac{{\log }_{3}4}{\sqrt{{\text{log}}_{3}4}}}=(3^{{\log }_{3}4}{)}^{\sqrt{{\log }_{4}3}}=4^{\sqrt{{\log }_{4}3}}$