The value of `(log_(3)81)` is:

Options

A. 0
B. 1
C. 2
D. 6

Answer

To find the value of \( \log_{3}81 \), we can follow these steps:

### Step 1: Rewrite 81 as a power of 3
First, we need to express 81 in terms of base 3. We know that:
\[ 81 = 3^4 \]

### Step 2: Apply the logarithmic identity
Next, we can use the property of logarithms that states:
\[ \log_{a}(b^k) = k \cdot \log_{a}(b) \]
In this case, we can apply this property:
\[ \log_{3}(81) = \log_{3}(3^4) \]

### Step 3: Simplify using the property
Using the property from Step 2, we can simplify:
\[ \log_{3}(3^4) = 4 \cdot \log_{3}(3) \]

### Step 4: Evaluate \( \log_{3}(3) \)
We know that:
\[ \log_{3}(3) = 1 \]
Thus, substituting this value back into our equation gives:
\[ \log_{3}(81) = 4 \cdot 1 = 4 \]

### Final Answer
Therefore, the value of \( \log_{3}(81) \) is:
\[ \boxed{4} \]

---