Answer: Third option.
Step-by-step explanation:
We need to remember these properties:
[tex]log_b(a)^n=nlog_b(a)\\\\log_b(b)=1\\\\\frac{1}{a}=a^{-1}[/tex]
Then, given the following expression:
[tex]log_2(\frac{1}{64} )[/tex]
You need to:
- Descompose 64 into its prime factors:
[tex]64=2*2*2*2*2*2=2^6[/tex]
- Substitute:
[tex]log_2(\frac{1}{2^6} )[/tex]
- Apply the properties shown above:
[tex]log_2(2)^{-6}=-6log_2(2)=-6(1)=-6[/tex]
