To convert the logarithmic equation \( \log_a a = 2x \) into exponential form, we need to recall the relationship between logarithms and exponents. The expression \( \log_a b = c \) can be rewritten in exponential form as \( a^c = b \).
In this specific case:
- The base \( a \) is raised to the power of \( 2x \),
- The result is \( a \).
So, the exponential form of the equation \( \log_a a = 2x \) is:
\[ a^{2x} = a \]
Next, we need to find \( x \) to evaluate \( \log_a a \). We can set the exponents equal to each other since the bases are the same (and \( a > 0 \), \( a \neq 1 \)):
\[ 2x = 1 \]
To solve for \( x \), divide both sides by 2:
\[ x = \frac{1}{2} \]
So, the value of \( x \) is \( \frac{1}{2} \). The evaluation of \( \log_a a \) is simply 1 since the logarithm of a number to its own base is always 1:
\[ \log_a a = 1 \]
Thus, the answers are:
- Exponential form: \( a^{2x} = a \)
- Value of \( x \): \( \frac{1}{2} \)