Question

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

Answer 1

Answer:

• C. - 6

Step-by-step explanation:

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

Correct choice is C

Answer 2

Answer:

-6

Step-by-step explanation:

Given expression:

$\log_2\left(\dfrac{1}{64}\right)$

$\textsf{Apply the log quotient law}: \quad \log_a\frac{x}{y}=\log_ax - \log_ay$

$\implies \log_21-\log_264$

$\textsf{Apply log law}: \quad \log_a1=0$

$\implies 0-\log_264$

$\implies -\log_264$

Rewrite 64 as 2⁶:

$\implies -\log_2(2^6)$

$\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax$

$\implies -6\log_22$

$\textsf{Apply log law}: \quad \log_aa=1$

$\implies -6 \cdot 1$

$\implies -6$

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