A) \[\sqrt{5}\]
B) 5
C) 26
D) 625
Correct Answer: D
Solution :
\[{{\log }_{1/4}}\beta =-\,1\] |
\[\Rightarrow \beta =4\] |
\[{{\log }_{\beta }}\alpha =-\,1\] |
\[\Rightarrow \alpha =\frac{1}{\beta }=\frac{1}{4}\] |
\[\gamma ={{\log }_{\alpha }}8={{\log }_{1/4}}8=-\frac{3}{2}\] |
Now \[\frac{1}{\alpha }+1=4+1=5\] |
\[{{\beta }^{2}}+4{{\gamma }^{2}}=16+4{{\left( -\frac{3}{2} \right)}^{2}}=25\] |
\[\therefore {{\left( \frac{1}{\alpha }+1 \right)}^{\log \sqrt{5}({{\beta }^{2}}+4{{\gamma }^{2}})}}\] |
\[={{5}^{{{\log }_{\sqrt{5}}}25}}=625\] |
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