Rewrite the exponential equation as a logarithmic equation.
$3^x=9$

• A. $\log_93=x$
• B. $\log_3x=9$
• C. $\log_33=9$
• D. $\log_{_3}9=x$

Answer: (D)

Verified step by step guidance

1. Understand that logarithms are the inverse operations of exponentiation. The expression \(\log_b(x) = y\) means that \(b^y = x\), where \(b\) is the base, \(x\) is the argument, and \(y\) is the logarithm.
2. Identify the base of the logarithm and the value inside the logarithm from the problem. For example, if you have \(\log_2(8)\), the base is 2 and the argument is 8.
3. Rewrite the logarithmic equation in its equivalent exponential form using the definition: \(\log_b(x) = y\) is equivalent to \(b^y = x\).
4. Solve the exponential equation for the unknown variable. This often involves recognizing powers of the base or using properties of exponents.
5. Check your solution by substituting back into the original logarithmic expression to ensure it satisfies the equation.