$32\root 5 \of 4 $ to the base $2\sqrt 2 = . . . .$

${(0.05)^{{{\log }_{_{\sqrt {20} }}}(0.1 + 0.01 + 0.001 + ......)}}= . .$ . .

${\log _2}7$ એ . . . . થાય.

જો ${\log _k}x.\,{\log _5}k = {\log _x}5,k \ne 1,k > 0$ તો $x = . . . .$

સમીકરણ $\left| {1 - {{\log }_{\frac{1}{6}}}x} \right| + \left| {{{\log }_2}x} \right| + 2 = \left| {3 - {{\log }_{\frac{1}{6}}}x + {{\log }_{\frac{1}{2}}}x} \right|$ નો ઉકેલગણ $\left[ {\frac{a}{b},a} \right],a,b, \in N,$ હોય તો $(a + b)$ ની કિમત મેળવો. 

${81^{(1/{{\log }_5}3)}} + {27^{{{\log }_{_9}}36}} + {3^{4/{{\log }_{_7}}9}} = . . . .$