Evaluate the given logarithm.
${\log }_{x}1$

• A. $x$
• B. $1$
• C. $0$
• D. $2$

Answer: (C)

Verified step by step guidance

1. Recall the definition of a logarithm: \(\log_{a} b = c\) means that \(a^{c} = b\).
2. Apply this definition to the problem: \(\log_{x} 1 = y\) means that \(x^{y} = 1\).
3. Consider the property of exponents that any nonzero number raised to the power of 0 equals 1, i.e., \(a^{0} = 1\) for \(a \neq 0\).
4. Since \(x^{y} = 1\), and \(x\) is the base (assumed to be positive and not equal to 1), the exponent \(y\) must be 0.
5. Therefore, \(\log_{x} 1 = 0\) because raising \(x\) to the power 0 gives 1.