Question

If $a={\log }_{10}25$ and $b={\log }_{10}36$ then value of is, $6^{a/b}+5^{b/a}-2=\lambda$ then $\sqrt{\lambda }=?$

Answer 1

We have,

$\begin{array}{c}a={\log }_{10}25b={\log }_{10}36\\ a=2{\log }_{10}5b=2{\log }_{10}6\\ \frac{a}{b}={\log }_{6}5\frac{b}{a}={\log }_{5}6\\ 6^{\frac{a}{b}}+5^{\frac{b}{a}}-2=6{\log }_{6}5+5{\log }_{5}6-2\\ =5+6-2=9\\ \lambda =9\\ \sqrt{\lambda }=3\end{array}$

Hence, this is the answer.