Question

Let $\quad A =\left(3^{\sqrt{\log _3 2}}\right)^{\sqrt{\log _2 3}}+\left(3^{\log _3 2}\right)^{\sqrt{\log _2 3}}+\left(3^{\sqrt{\log _3 2}}\right)^{\sqrt{\log _3 2}}$ and $\quad B=\left(2^{\sqrt{\log _3 2}}\right)^{\sqrt{\log _2 3}}+\left(2^{\log _2 3}\right)^{\sqrt{\log _3 2}}-\left(2^{\sqrt{\log _2 3}}\right)^{\sqrt{\log _2 3}}$. Then find the value of $(A-B)$.

Answer 1

$A =3^1+2^{\sqrt{\log _2 3}}+2 ; \quad B =2+3^{\sqrt{\log _3 2}}-3$
Hence, $(A-B)=6$