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Logarithm Of The Nested Radical

Algebra Level 2

$\large \log_{\sqrt{x}} \left( \sqrt{x\sqrt{x\sqrt{x\sqrt{x}}}} \right) = \, ?$

Clarification: $x$ is a positive real number and $x \neq 1.$

\frac{15}2

\frac{15}{4}

\frac{15}8

\frac{15}{16}

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by Abhiram Rao

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