Question

Let $A={\left(3^{\sqrt{{\log }_{3}2}}\right)}^{\sqrt{{\log }_{2}3}}+{\left(3^{{\log }_{3}2}\right)}^{\sqrt{{\log }_{2}3}}+{\left(3^{\sqrt{{\log }_{3}2}}\right)}^{\sqrt{{\log }_{3}2}}$ and $B={\left(2^{\sqrt{{\log }_{3}2}}\right)}^{\sqrt{{\log }_{2}3}}+{\left(2^{{\log }_{2}3}\right)}^{\sqrt{{\log }_{3}2}}-{\left(2^{\sqrt{{\log }_{2}3}}\right)}^{\sqrt{{\log }_{2}3}}$. Then find the value of $(A-B)$.

Answer 1

Answer: 6

$A=3^1+2^{\sqrt{{\log }_{2}3}}+2;B=2+3^{\sqrt{{\log }_{3}2}}-3$
Hence, $(A-B)=6$