Solve log₉(74) + log₉(1/2): Logarithm Addition Problem

To solve this problem, we'll apply the following steps:

• Step 1: Identify given logarithms and their base.
• Step 2: Employ the sum of logarithms property to combine the terms.
• Step 3: Calculate the resulting argument of the logarithm.

Now, let's work through each step:

Step 1: We have two logarithms: $\log_9 74$ and $\log_9 \frac{1}{2}$, sharing the base of $9$.

Step 2: Since the bases are the same, we use the sum property of logarithms:

$\log_9 74 + \log_9 \frac{1}{2} = \log_9 (74 \times \frac{1}{2})$.

Step 3: Calculate the product $74 \times \frac{1}{2}$:

$74 \times \frac{1}{2} = 37$.

So, we have:

$\log_9 (74 \times \frac{1}{2}) = \log_9 37$.

Therefore, the solution to the problem is $\log_9 37$.