Solve 1/log₄(9): Simplifying Reciprocal Logarithm Expression

$\frac{1}{\log_49}=$

To solve this problem, we'll follow these steps:

• Step 1: Identify the property of logarithms that relates inverses.
• Step 2: Apply this property to the given expression.
• Step 3: Compare with provided choices to identify the correct option.

Now, let's work through each step:

Step 1: The problem asks us to find the expression equal to $\frac{1}{\log_4 9}$.

Step 2: We use the logarithmic property $\log_b a = \frac{1}{\log_a b}$. Thus, replacing $b$ with 9 and $a$ with 4, we have:

$\frac{1}{\log_4 9} = \log_9 4$.

Step 3: Comparing this result to the provided choices, we find that the correct answer is $\log_9 4$, corresponding to Choice 1.

Therefore, the solution to the problem is $\log_9 4$.