Question

evaluate the logarithm without the use of a calculator.
\\(\log_{8} 1 = \square\\)

Explanation:

Step1: Recall 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 non - zero \( a \), and by the definition of a logarithm \( \log_a x = y \) is equivalent to \( a^y = x \). When \( x = 1 \), we need to find \( y \) such that \( a^y=1 \), and the solution to this equation is \( y = 0 \) (since any non - zero number raised to the power of 0 is 1).

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

Using the property \( \log_a 1=0 \) (where \( a = 8\) and \( 8>0, 8
eq1\)), we can directly say that \( \log_8 1 = 0 \).

Answer:

\( 0 \)