`log_a(mn)` is equal to :

Options

A. `nlog_a(m)`
B. `log_amxxlog_an`
C. `log_am+log_an`
D. `log_am-log_an`

Answer

To solve the problem `log_a(mn)`, we can use the properties of logarithms. Here’s a step-by-step solution:

### Step 1: Understand the Logarithm Property
We need to recall the property of logarithms that states:
\[ \log_a(mn) = \log_a(m) + \log_a(n) \]
This property allows us to break down the logarithm of a product into the sum of the logarithms.

### Step 2: Apply the Property
Using the property mentioned above, we can express `log_a(mn)` as:
\[ \log_a(mn) = \log_a(m) + \log_a(n) \]

### Step 3: Write the Final Answer
Thus, we conclude that:
\[ \log_a(mn) = \log_a(m) + \log_a(n) \]

### Final Answer
The expression `log_a(mn)` is equal to `log_a(m) + log_a(n)`.

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