Question

convert log equation to exponential (numeric)
question
write the logarithmic equation as an exponential equation.
\\(\log_{2}(\sqrt{2}) = \frac{1}{2}\\)

Explanation:

Step1: Recall log - exp conversion rule

The rule for converting $\log_{a}b = c$ to exponential form is $a^{c}=b$.

Step2: Identify values of a, b and c

In the given equation $\log_{2}(\sqrt{2})=\frac{1}{2}$, we have $a = 2$, $b=\sqrt{2}$, and $c=\frac{1}{2}$.

Step3: Write exponential equation

Using the rule $a^{c}=b$, we get $2^{\frac{1}{2}}=\sqrt{2}$.

Answer:

$2^{\frac{1}{2}}=\sqrt{2}$