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

Matilda Fox

Matilda Fox

Answered question

2022-07-18

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 )

Answer & Explanation

kartonaun

kartonaun

Beginner2022-07-19Added 14 answers

Yes and this is equal to
6 log 6 ( 11 ) + 1 3 ( log ( 2 ) + 1 )
Bruno Thompson

Bruno Thompson

Beginner2022-07-20Added 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 )

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?