Final answer:
The value of log₂ 64 is 6, because 2 raised to the power of 6 equals 64.
Step-by-step explanation:
The value of log₂ 64 can be determined by asking what power you must raise 2 to in order to get 64. Since 26 = 64, the logarithm of 64 with a base of 2 is 6. This could also be approached using the property of logarithms where if ax = b, then logab = x. So, in this case, since 26 = 64, it follows that log₂ 64 = 6.
The logarithm of 64 to the base 2, denoted as log₂ 64, signifies the exponent to which the base (2) must be raised to obtain the number 64.
Evaluating this logarithm, 2 raised to the power of 6 is equal to 64 (2⁶ = 64). Therefore, the value of log₂ 64 is indeed 6, as 2 raised to the exponent 6 results in 64.
This can also be interpreted as the logarithmic property, where if \( a^x = b \), then \( \log_{a}b = x \). Applying this property, since \( 2^6 = 64 \), it follows that \( \log_{2}64 = 6 \). Hence, both the direct evaluation and the logarithmic property demonstrate that the value of log₂ 64 is 6.