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Question Number 19171 by gourav~ last updated on 06/Aug/17

$${log}_{\sqrt{2}}\sqrt{2\sqrt{2\sqrt{2\sqrt{2}}}}$$

Commented by gourav~ last updated on 06/Aug/17

$$findvalue$$

Answered by Tinkutara last updated on 06/Aug/17

$$\sqrt{2\sqrt{2\sqrt{2\sqrt{2}}}}=2^{\frac{2^4-1}{2^4}}=2^{\frac{15}{16}}={\left(\sqrt{2}\right)}^{\frac{15}{8}}$$$${\log }_{\sqrt{2}}{\left(\sqrt{2}\right)}^{\frac{15}{8}}=\frac{15}{8}$$

Commented by Tinkutara last updated on 06/Aug/17

$$\mathrm{See}\mathrm{Q}.18551.$$

Commented by chernoaguero@gmail.com last updated on 06/Aug/17

$$sirhowdidu\frac{2^4-1}{2^4}plzbesimplistic$$

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