If x=12 log4 then log2(x/4) what is the value of x? Answer me step by step
Share
If x=12 log4 then log2(x/4) what is the value of x? Answer me step by step
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Hey Buddy
Here's The Answer
_____________________________
Properties Used :
i. log a - log b = log ( a/b )
ii. logₐ a = 1
iii. logₐ b = x , can be written as b = aˣ
iv. log aᵇ = b × log a
Given : log₄ ( x ) = 12
By property ( iii )
=> log₄ ( x ) = 12
=> x = 4¹²
To Find : log₂ ( x/4 )
SOLUTION :
=> log₂ ( x/4 )
By property ( i )
=> log₂ ( x ) - log₂ ( 4 ) ___ ( 1 )
Putting ( x = 4¹² ) in eqn ( 1 )
=> log₂ ( 4¹² ) - log₂ ( 2² )
=> log₂ ( 2²⁴ ) - log₂ ( 2² )
By property ( iv )
=> 24 × log₂ ( 2 ) - 2 ×log₂ ( 2 )
By property ( ii )
=> 24 - 2
=> 22
Hope It Helps.