Question

simplify.
$3^{\log_{3}(966)}$
$3^{\log_{3}(966)} = \square$

Explanation:

Step1: Recall the inverse property of logarithms

For any positive number \( a \) (where \( a
eq 1 \)) and any positive number \( x \), the property \( a^{\log_{a}(x)}=x \) holds. This is because the logarithm \( \log_{a}(x) \) represents the exponent to which \( a \) must be raised to get \( x \), so raising \( a \) to that exponent gives back \( x \).

Step2: Apply the property to the given expression

In the expression \( 3^{\log_{3}(966)} \), we have \( a = 3 \) and \( x = 966 \). Using the property \( a^{\log_{a}(x)}=x \), we can directly conclude that \( 3^{\log_{3}(966)}=966 \).

Answer:

\( 966 \)