Does the following expand to the following log_6(11^6root[3](12)) = 6 log_6(11) + log_6 (root[3](12))

Matilda Fox 2022-07-18 Answered
Expansion of Logarithms with Cube Roots
Does the following expand to the following
log 6 ( 11 6 12 3 )
= 6 log 6 ( 11 ) + log 6 ( 12 3 )
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Answers (2)

kartonaun
Answered 2022-07-19 Author has 14 answers
Yes and this is equal to
6 log 6 ( 11 ) + 1 3 ( log ( 2 ) + 1 )
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Bruno Thompson
Answered 2022-07-20 Author has 9 answers
First note that
x n = x 1 n
log b ( x y ) = log b ( x ) + log b ( y )
log b ( x n ) = n log b ( x )
log b ( x ) = log 10 ( x ) log 10 ( b ) = log ( x ) log ( b )
So then
log 6 ( 11 6 12 3 ) = log 6 ( 11 6 12 1 3 ) = log 6 ( 11 6 ) + log 6 ( 12 1 3 ) = 6 log 6 ( 11 ) + 1 3 log 6 ( 12 )
Or perhaps
6 log ( 11 ) log ( 6 ) + log ( 12 ) 3 log ( 6 )
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