Question

$\log_{7} \log_{7} \sqrt{7 (\sqrt{7 \sqrt{7}})} =$

Easy

Solution

$\log_{7} \log_{7} \sqrt{7 \sqrt{7 \sqrt{7}}} = \log_{7} \log_{7} 7^{7 / 8} = \log_{7} (7 / 8)$
$= \log_{7} 7 - \log_{7} 8 = 1 - \log_{7} 2^{3} = 1 - 3 \log_{7} 2 .$

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