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100 POINTS Solve log base 2 of one over sixty four. negative one sixth one sixth −6 6

Sagot :

Mhanifaidn

Answer:

  • C. - 6

Step-by-step explanation:

  • log₂(1/64) =
  • log₂(1/2⁶) =
  • log₂(2⁻⁶) =
  • -6

Correct choice is C

Semsee45idn

Answer:

-6

Step-by-step explanation:

Given expression:

[tex]\log_2\left(\dfrac{1}{64}\right)[/tex]

[tex]\textsf{Apply the log quotient law}: \quad \log_a\frac{x}{y}=\log_ax - \log_ay[/tex]

[tex]\implies \log_21-\log_264[/tex]

[tex]\textsf{Apply log law}: \quad \log_a1=0[/tex]

[tex]\implies 0-\log_264[/tex]

[tex]\implies -\log_264[/tex]

Rewrite 64 as 2⁶:

[tex]\implies -\log_2(2^6)[/tex]

[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies -6\log_22[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies -6 \cdot 1[/tex]

[tex]\implies -6[/tex]

Learn more about log laws here:

https://brainly.com/question/27963321

https://brainly.com/question/27953288

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