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Jimbobuk asked Nov 14, 2023

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9 votes

True or false? Show steps

Mathematics
college

Jimbobuk asked Nov 14, 2023

by Jimbobuk

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11 votes

Answer:

TRUE

Explanation:

Consider

$log_( √(x) )( {x}^(k) )$

$log_( √(x) )( {( √(x) }^(2))^(k) )$

$log_( √(x) ){( √(x))^(2k) } )$

we know that

$log( {a}^(b) ) = b log(a)$

===

2k (log_( √(x) )( √(x) ) )

Also we know that

log_(a)(a) = 1

===

2k( log_( √(x) )( √(x) ) = 2k * 1 = 2k

Hence

$log_( √(x) )( {x}^(k) ) = 2k$

Therefore it TRUE

Chetan Arvind Patil answered Nov 20, 2023

by Chetan Arvind Patil

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