উদাহরণ ৫৷ প্রমান করো 
[H.S’93]
প্রমান: মনে করি
অতএব
x = \sqrt {5\sqrt {5\sqrt {5 \ldots \ldots \infty } } } \\
\Rightarrow {x^2} = 5\sqrt {5\sqrt {5\sqrt {5 \ldots \ldots \infty } } } \\
\Rightarrow {x^2} = 5x\\
\Rightarrow {x^2} - 5x = 0\\
\Rightarrow x\left( {x - 5} \right) = 0\\
\Rightarrow x = 5\left( {x \ne 0} \right)
\end{array}" alt="\begin{array}{l}
x = \sqrt {5\sqrt {5\sqrt {5 \ldots \ldots \infty } } } \\
\Rightarrow {x^2} = 5\sqrt {5\sqrt {5\sqrt {5 \ldots \ldots \infty } } } \\
\Rightarrow {x^2} = 5x\\
\Rightarrow {x^2} - 5x = 0\\
\Rightarrow x\left( {x - 5} \right) = 0\\
\Rightarrow x = 5\left( {x \ne 0} \right)
\end{array}"/>
-br /-\end{array}.jpg "\begin{array}{l}<br />{\log _5}\sqrt {5\sqrt {5\sqrt {5 \ldots \ldots \infty } } } \\<br /> = {\log _5}x\\<br /> = {\log _5}5\\<br /> = 1\left( {proved} \right)<br />\end{array}")
