Question

The value of log7 [log7 √7√7√7 ] is :​

Answer 1

Answer:

log7 [log7 √7√7√7 ]

= log 7 [ log 7 * √7³]

= log 7 [ log 7 + log √7³]

= log 7 [ log 7 ] +  log 7 [ log √7³]

= ( log 7 )² + log7 [ log 7 ^ 3/2 ]

= ( log 7 )² + 3/2 *  ( log 7 )²

= ( log 7 )² ( 1 + 3/2 )

= ( log 7 )² ( 5/2 )

=( 5/2 )( log 7 )²

= 1.785 ( answer )

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Answer 2

Answer:

$\huge\bf\underline\red{Correct Question}$

$\bf\blue{ log_{7}[ log_{7} \sqrt{7 \sqrt{7 \sqrt{7} } }] \: is \: equal \: to \: ?}$

$\huge\bf\underline\green{Solution:}$

$\bf\orange{ log_{7}( log_{7} \sqrt{7 \sqrt{7 \sqrt{7} } } ) }$

$\bf\red{\implies log_{7}( log_{7} \sqrt{7 \sqrt{ {7}^{ \frac{3}{2} } } } )}$

$\bf\green{\implies log_{7}( log_{7} \sqrt{ { 7}^{1 + \frac{3}{4} } } )}$

$\bf\purple{\implies log_{7}( log_{7} {7}^{ \frac{7}{8} } )}$

$\bf\pink{\implies log_{7} \frac{7}{8} = log_{7}\:7-log_{7}\:8 }$

$\bf\orange{ \implies 1 - 3 \: log_{7} \: 2 }$