Question

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

• A. $3\log_{2}7$
• B. $1 - 3\log_{3}7$
• C. $1 - 3\log_{7}2$
• D. None of these

Answer 1

Answer: (C)

$1 - 3\log_{7}2$

Answer 2

$\log_{7}{\log_{7}\sqrt{7\sqrt{7\sqrt{7}}}} = \log_{7}{\log_{7}7^{7/8}} = \log_{7}(7/8)$

$= \log_{7}7 - \log_{7}8 = 1 - \log_{7}2^{3} = 1 - 3\log_{7}2$.