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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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