Evaluate: log _7(log _7sqrt {7sqrt {7sqrt 7 } | vedclass

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Question

(C) Let $x = \sqrt{7\sqrt{7\sqrt{7}}}$.We can write this as $x = 7^{1/2} \cdot 7^{1/4} \cdot 7^{1/8} = 7^{(1/2 + 1/4 + 1/8)} = 7^{7/8}$.Now,the expres

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$1 - 3\log _72$

Vedclass · Answer

(C) Let $x = \sqrt{7\sqrt{7\sqrt{7}}}$.We can write this as $x = 7^{1/2} \cdot 7^{1/4} \cdot 7^{1/8} = 7^{(1/2 + 1/4 + 1/8)} = 7^{7/8}$.Now,the expression is $\log_7(\log_7(7^{7/8}))$.Using the property $\log_b(b^a) = a$,we get $\log_7(7/8)$.This is equal to $\log_7(7) - \log_7(8) = 1 - \log_7(2^3)$.Using the power rule $\log(a^n) = n\log(a)$,we get $1 - 3\log_7(2)$.

Evaluate: $\log _7(\log _7\sqrt {7\sqrt {7\sqrt 7 } }) = $

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