How do you solve this logarithm? Solve for x in the following: x = 9 <

dresu9dnjn

dresu9dnjn

Answered question

2022-05-13

How do you solve this logarithm?
Solve for x in the following:
x = 9 log 3 ( 2 )
The answer is 4, but why?

Answer & Explanation

Duncan Cox

Duncan Cox

Beginner2022-05-14Added 18 answers

Well, 9 = 3 2 . So what we really have is
x = 9 log 3 2 = ( 3 2 ) log 3 2 = 3 2 log 3 2 = 3 log 3 2 2
But then that is
x = 3 log 3 2 2 = 3 log 3 4 = 4
3c4ar1bzki1u

3c4ar1bzki1u

Beginner2022-05-15Added 4 answers

9 log 3 2 = ( 3 2 ) log 3 2 = 3 2 ( log 3 2 )
now use the logarithmic identity x log n b = l o g n b x to get:
3 2 ( log 3 2 ) = 3 ( log 3 2 2 ) = 3 ( log 3 4 ) = 4

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