Log_7 log_7 √(7 √(7 √(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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Fundamental Laws of Logarithms

log7 log7 √7 ...

Question

$l o g_{7} l o g_{7} \sqrt{7 (\sqrt{7 \sqrt{7}})} =$

3 l o g_{2} 7

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1 - 3 l o g_{3} 7

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1 - 3 l o g_{7} 2

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Solution

The correct option is C $1 - 3 l o g_{7} 2$
$l o g_{7} l o g_{7} \sqrt{7 \sqrt{7 \sqrt{7}}} = l o g_{7} l o g_{7} 7^{\frac{7}{8}} = l o g_{7} (\frac{7}{8})$
$= l o g_{7} 7 - l o g_{7} 8 = 1 - l o g_{7} 2^{3} = 1 - 3 l o g_{7} 2$

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Similar questions

{log}_{7} {log}_{7} \sqrt{7 \sqrt{7 \sqrt{7}}}

{lim}_{x \to 7} \frac{log x - log 7}{x - 7}

f (x) = \begin{matrix} \frac{log x - log 7}{x - 7}, & f o r x \neq 7 = 7, & f o r x = 7 \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭

x = 7

f (x) = \frac{l o g x - l o g 7}{x - 7}

x \neq 7

f (x) = ⎧ ⎨ ⎩ \begin{matrix} \frac{log x - log 7}{x - 7} & for x \neq 7 7, & for x = 7 \end{matrix}

x = 7

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