Question

log 1/16 to the. base 2

Answer 1

Hey there!

Refer Attachment

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Answer 2

Therefore the value of ㏒₂ ( 1 / 16 ) is -4.

Given:

Given logarithmic number = ㏒₂ ( 1 / 16 )

To Find:

The value of ㏒₂ ( 1 / 16 )

Solution:

The given question can be solved as shown below.

Given logarithmic number = ㏒₂ ( 1 / 16 )

⇒ ㏒₂ ( 1 / 16 ) = ㏒₂ ( 1 / 2⁴ )

⇒ ㏒₂ ( 1 / 2⁴ ) = ㏒₂ 1 - ㏒₂ 2⁴    ( ∵ log ( a/b ) = log a - log b )

⇒ ㏒₂ ( 1 / 2⁴ ) = ㏒₂ 1 - 4㏒₂ 2    ( ∵ log aᵇ = a log b )

⇒ ㏒₂ ( 1 / 2⁴ ) = 0 - 4 ( 1 )     ( ∵  ㏒₂ 1 =0 and ㏒₂ 2 = 1 )

⇒ ㏒₂ ( 1 / 2⁴ ) = -4

Therefore the value of ㏒₂ ( 1 / 16 ) is -4.

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