Answer
11.
Work Step by Step
The logarithm, base a, of a is 1.
${{\log }_{a}}a=1$
And the power rule for a logarithmic function is:
${{\log }_{a}}{{\left( m \right)}^{n}}=n{{\log }_{a}}\left( m \right)$
Here, $m\text{ and }a$ are positive real numbers, $a\ne 1$ and $n$ can be any real number.
Calculation:
Consider the logarithmic expression.
${{\log }_{2}}{{2}^{11}}$
${{\log }_{2}}{{2}^{11}}=11{{\log }_{2}}2$
This gives:
$\begin{align}
& {{\log }_{2}}{{2}^{11}}=11\left( 1 \right) \\
& =11
\end{align}$
Thus, the value of ${{\log }_{2}}{{2}^{11}}$ is 11.
