Logarithm with nth root I made it but the result is very strange. I want every step to the result 6log_(10)((sqrt2)/(root[3](3+ sqrt5)))

Messiah Sutton

Messiah Sutton

Answered question

2022-11-08

Logarithm with nth root
I made it but the result is very strange. I want every step to the result
6 log 10 2 3 + 5 3

Answer & Explanation

Emma Singleton

Emma Singleton

Beginner2022-11-09Added 11 answers

Here is an alternate approach from the first answer:
6 log 10 2 3 + 5 3 = log 10 ( 2 3 + 5 3 ) 6 = log 10 2 3 ( 3 + 5 ) 2 = log 10 8 14 + 6 5 = log 10 4 7 + 3 5 = log 10 4 7 + 3 5 7 3 5 = log 10 4 ( 7 3 5 ) 49 45 = log 10 ( 7 3 5 )
inurbandojoa

inurbandojoa

Beginner2022-11-10Added 11 answers

I assume that the question is how to expand the logarithm. Note that
6 log 10 ( 2 3 + 5 3 ) = 6 log 10 ( 2 ) 6 log 10 ( 3 + 5 3 ) = 6 log 10 ( 2 1 / 2 ) 6 log 10 ( ( 3 + 5 ) 1 / 3 ) = 6 1 2 log 10 2 6 1 3 log 10 ( 3 + 5 ) = 3 log 10 2 2 log 10 ( 3 + 5 )

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