Question

evaluate the following expression. you should do this problem without a calculator.
\\(\log_{6} 6\\)
\\(\bigcirc\\) a. 1
\\(\bigcirc\\) b. 12
\\(\bigcirc\\) c. 6
\\(\bigcirc\\) d. 0

Explanation:

Step1: Recall the logarithm identity

The logarithm identity states that for any positive real number \( a \) (where \( a
eq 1 \)), \( \log_a a = 1 \). This is because the logarithm \( \log_a x \) represents the exponent to which we must raise \( a \) to get \( x \). In this case, we want to find the exponent \( y \) such that \( a^y = x \). For \( \log_6 6 \), we set \( 6^y = 6 \).

Step2: Solve for the exponent

We know that any non - zero number raised to the power of 1 is itself. So, if \( 6^y = 6 \), then \( y = 1 \). Therefore, \( \log_6 6=1 \).

Answer:

A. 1