Question

evaluate the expression without using a calculator.
\\(\log_{8}1\\)
\\(\log_{8}1 = \square\\)
(type an integer or a simplified fraction.)

Explanation:

Step1: Recall the logarithm property

The logarithm property states that for any positive real number \( a \) (where \( a
eq 1 \)), \( \log_a 1 = 0 \). This is because \( a^0 = 1 \) for any \( a>0, a
eq 1 \), and the logarithm \( \log_a x \) is the exponent to which \( a \) must be raised to get \( x \).

Step2: Apply the property to \( \log_8 1 \)

Using the property \( \log_a 1 = 0 \) with \( a = 8 \), we get \( \log_8 1 = 0 \).

Answer:

\( 0 \)