Questions: Simplify the expression without using a calculator. log(π) 1=

Solution Steps

To simplify the expression \(\log_{\pi} 1\), we need to recall the logarithmic identity that states \(\log_b a = c\) if and only if \(b^c = a\). In this case, we are looking for the value of \(c\) such that \(\pi^c = 1\). Since any number raised to the power of 0 is 1, the value of \(\log_{\pi} 1\) is 0.

To simplify the expression \( \log_{\pi} 1 \), we use the logarithmic identity that states \( \log_b a = c \) if and only if \( b^c = a \). Here, we need to find \( c \) such that \( \pi^c = 1 \).

Since any number raised to the power of 0 equals 1, we have: \[ \pi^0 = 1 \] Thus, it follows that: \[ \log_{\pi} 1 = 0 \]

Final Answer