Question

question 7 (1 point)
evaluate \\(\log_{4} \frac{1}{64}\\).
\\(\bigcirc\\) a) -3
\\(\bigcirc\\) b) -8
\\(\bigcirc\\) c) 3
\\(\bigcirc\\) d) 8

Explanation:

Step1: Recall logarithm definition

Let \( \log_{4}\frac{1}{64} = x \). By definition of logarithm, \( 4^x=\frac{1}{64} \).

Step2: Express 64 as power of 4

We know \( 64 = 4^3 \), so \( \frac{1}{64}=\frac{1}{4^3}=4^{-3} \).

Step3: Solve for x

Now we have \( 4^x = 4^{-3} \). Since the bases are equal, the exponents must be equal, so \( x=-3 \).

Answer:

a) -3