Question

which logarithmic equation is equivalent to (3^2 = 9)?

(2 = \log_3 9)
(2 = \log_9 3)
(3 = \log_2 9)
(3 = \log_9 2)

Explanation:

⚡ Using what you learned: Understanding Logarithmic Functions

Step 1: Identify the components of the exponential equation

The given exponential equation is:

$$ 3^2 = 9 $$

Here:

• The base is \( b = 3 \)
• The exponent is \( x = 2 \)
• The result is \( y = 9 \)

Step 2: Convert to logarithmic form

The general relationship between an exponential equation and its logarithmic form is:

$$ b^x = y \iff \log_b(y) = x $$

Substituting our values:

$$ \log_3(9) = 2 $$

Which can be written as:

$$ 2 = \log_3 9 $$

Answer:

\( 2 = \log_3 9 \)