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. Recognize the expression given: \$5^{\log_5 12}$. This means 5 raised to the power of the logarithm base 5 of 12.
2. Recall the fundamental property of logarithms and exponents: for any positive number \(a \neq 1\) and any positive number \(x\), \(a^{\log_a x} = x\).
3. Apply this property directly to the expression \$5^{\log_5 12}$, which simplifies the expression to just the argument of the logarithm, which is 12.
4. Understand that this simplification works because the logarithm base 5 of 12 asks the question: 'To what power must 5 be raised to get 12?' Raising 5 to that power returns 12.
5. Therefore, the value of the expression \$5^{\log_5 12}$ is simply 12.