Question

\[\log_{\,2}{\dfrac{1}{64}}\] =

Answer 1

The value of \(\log_{\,2}{\frac{1}{64}}\) is -6, as 64 is a power of 2 (specifically, 2 to the power of 6) and using the properties of logarithms.

Step-by-step explanation:

To calculate the value of \(\log_{\,2}{\dfrac{1}{64}}\),

we can use the properties of logarithms and the concept that a negative logarithm indicates a number less than 1.

Since 64 is a power of 2, namely \(2^6\), we can rewrite the fraction inside the logarithm as \(2^{-6}\).

Thus, \(\log_{\,2}{2^{-6}}\) is simply -6 because the base of the logarithm and the base of the exponent inside are the same.