The correct option is D 1 3 log_7 2log_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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Inverse of a Function

log 7log 7√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}}}

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

{log}_{7} ({log}_{7} \sqrt{7 (\sqrt{7 \sqrt{7}})})

{log}_{7} {log}_{7} \sqrt{7 \sqrt{(7 \sqrt{7})}} = 1 - 3 {log}_{7} 2

Find the value of ${log}_{7} {log}_{7}$ $\sqrt{7 (\sqrt{7 \sqrt{7}})}$ , if ${log}_{10}$ 7 = 0.8450 and ${log}_{10}$ 2 = 0.3010

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