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

• A. $x$
• B. $1$
• C. $0$
• D. $2$

Answer: (C)

Verified step by step guidance

1. Identify the specific logarithmic expression or equation you need to simplify or solve. Since the problem mentions 'Basic Properties of Logarithms,' recall the key properties such as the product rule, quotient rule, and power rule.
2. Write down the relevant logarithm properties: - Product Rule: \(\log_b (MN) = \log_b M + \log_b N\) - Quotient Rule: \(\log_b \left(\frac{M}{N}\right) = \log_b M - \log_b N\) - Power Rule: \(\log_b (M^p) = p \log_b M\)
3. Apply these properties step-by-step to the given logarithmic expression. For example, if you have a product inside the log, split it into a sum of logs; if you have a quotient, split it into a difference; if you have an exponent, bring it in front as a multiplier.
4. After rewriting the expression using the properties, combine like terms if possible. This might involve adding or subtracting logarithms with the same base or simplifying coefficients.
5. If the problem involves solving for a variable inside the logarithm, rewrite the logarithmic equation in its exponential form using the definition \(\log_b A = C \iff b^C = A\), then solve the resulting equation algebraically.