Question

Which of the following is equal to log2 8^4/3
?(1 point)
Responses

16/3
Start Fraction 16 over 3 End Fraction

9/4

Start Fraction 9 over 4 End Fraction

64/3
Start Fraction 64 over 3 End Fraction

4

Answer 1

To solve for \( \log_2 \left( \frac{8^{4/3}}{1} \right) \), we can first simplify the expression inside the logarithm.

1. Rewrite \( 8 \) as \( 2^3 \):
\[
8^{4/3} = (2^3)^{4/3}
\]

2. Use the power of a power property of exponents:
\[
(2^3)^{4/3} = 2^{3 \cdot \frac{4}{3}} = 2^4
\]

3. Now, we can find \( \log_2(2^4) \):
\[
\log_2(2^4) = 4
\]

Thus, \( \log_2 \left( \frac{8^{4/3}}{1} \right) = 4 \).

The answer is \( \boxed{4} \).