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Sagot :
Answer:
- C. - 6
Step-by-step explanation:
- log₂(1/64) =
- log₂(1/2⁶) =
- log₂(2⁻⁶) =
- -6
Correct choice is C
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:
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