Question

Which of the following is equal to
log
2
8
4
3
?(1 point)
Responses

4
4

9
4

Start Fraction 9 over 4 End Fraction

64
3
Start Fraction 64 over 3 End Fraction

16
3

Answer 1

To solve the expression \( \log_{2} \left(\frac{8}{4}\right)^{3} \), we can simplify it step by step.

1. Simplify the fraction inside the logarithm:
\[
\frac{8}{4} = 2
\]

2. Substitute back into the logarithm:
\[
\log_{2} (2^{3})
\]

3. Use the logarithm power rule \( \log_{b} (a^{c}) = c \cdot \log_{b} (a) \):
\[
= 3 \cdot \log_{2} (2)
\]

4. Since \( \log_{2} (2) = 1 \):
\[
= 3 \cdot 1 = 3
\]

Now, looking at your response options, none of them equal to 3. Please check if there is a misinterpretation of the given expression. If the expression stands as is, then the solution is \( 3 \).