Question

evaluate the expression without using a calculator.
\\(\log_{7} 1\\)
\\(\log_{7} 1 = \square\\)
(type an integer or a simplified fraction.)

Explanation:

Step1: Recall the logarithm property

The logarithm property states that for any base \( a > 0, a
eq1 \), \( \log_{a}1 = 0 \). This is because \( a^{0}=1 \) for any non - zero real number \( a \), and by the definition of a logarithm \( \log_{a}x = y \) if and only if \( a^{y}=x \).

Step2: Apply the property to \( \log_{7}1 \)

Using the property \( \log_{a}1 = 0 \) with \( a = 7 \), we get \( \log_{7}1=0 \).

Answer:

\( 0 \)