If `log_(3)a=4`, find value of a.

Options

A. A)27
B. B)3
C. C)9
D. D)81

Answer

To solve the problem where \( \log_{3} a = 4 \), we can use the property of logarithms that states:

If \( \log_{b} x = y \), then \( x = b^{y} \).

### Step-by-Step Solution:

1. **Identify the logarithmic equation**: We start with the equation given in the problem:
\[ \log_{3} a = 4 \]

2. **Apply the property of logarithms**: According to the property mentioned, we can rewrite the equation in exponential form:
\[ a = 3^{4} \]

3. **Calculate \( 3^{4} \)**: Now we need to compute \( 3^{4} \):
\[ 3^{4} = 3 \times 3 \times 3 \times 3 \]
- First, calculate \( 3 \times 3 = 9 \).
- Next, calculate \( 9 \times 3 = 27 \).
- Finally, calculate \( 27 \times 3 = 81 \).

Thus, \( 3^{4} = 81 \).

4. **Conclusion**: Therefore, the value of \( a \) is:
\[ a = 81 \]

### Final Answer:
The value of \( a \) is \( 81 \).

---