Evaluate the given expression.
$5^{{\log }_{5}12}$

• A. $12$
• B. $5.40$
• C. $41.94$
• D. $96.57$

Answer: (A)

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 Practice,' recall the key properties such as the product, quotient, and power rules.
2. Apply the product rule: \(\log_b(MN) = \log_b(M) + \log_b(N)\), the quotient rule: \(\log_b\left(\frac{M}{N}\right) = \log_b(M) - \log_b(N)\), or the power rule: \(\log_b(M^p) = p \cdot \log_b(M)\), depending on the structure of the given logarithmic expression.
3. Rewrite the logarithmic expression step-by-step using these properties to combine or break apart the logs. For example, if you have a product inside the log, split it into a sum of logs; if you have a quotient, write it as a difference.
4. If the problem involves solving a logarithmic equation, after simplifying the logs, rewrite the equation in exponential form using the definition \(\log_b(A) = C \iff b^C = A\) to isolate the variable.
5. Finally, solve the resulting algebraic equation for the variable, and check your solution to ensure it is within the domain of the original logarithmic expression (i.e., arguments of all logarithms must be positive).