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

• A. ${\log }_{9}3=x$
• B. ${\log }_{3}x=9$
• C. ${\log }_{3}3=9$
• D. ${\log }_{{}_3}9=x$

Answer: (D)

Verified step by step guidance

1. Recall the relationship between exponential and logarithmic forms: if \(a^{x} = b\), then the equivalent logarithmic form is \(\log_{a} b = x\).
2. Identify the base \(a\), the exponent \(x\), and the result \(b\) in the given exponential equation \$3^{x} = 9$.
3. Here, the base \(a\) is 3, the exponent is \(x\), and the result \(b\) is 9.
4. Rewrite the equation in logarithmic form by placing the base 3 as the base of the logarithm, the result 9 as the argument of the logarithm, and set it equal to the exponent \(x\).
5. The logarithmic form is therefore \(\log_{3} 9 = x\).