Question

If x=12 log4 then log2(x/4) what is the value of x? Answer me step by step​

Answer 1

Hey Buddy

Here's The Answer

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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.