Question

evaluate the following expression without using a calculator.\\(\log_{2}(\sqrt{2})\\)\\(\log_{2}(\sqrt{2}) = \square\\)

Explanation:

Step1: Rewrite the square root as an exponent

Recall that $\sqrt{2} = 2^{\frac{1}{2}}$. So we can rewrite the logarithm as $\log_{2}(2^{\frac{1}{2}})$.

Step2: Apply the logarithm power rule

The power rule of logarithms states that $\log_{a}(a^{x}) = x$ for any positive real number $a
eq1$ and real number $x$. Here, $a = 2$ and $x=\frac{1}{2}$, so $\log_{2}(2^{\frac{1}{2}})=\frac{1}{2}$.

Answer:

$\frac{1}{2}$