If `f(x)=log_(6)x and f(2)=0.231`, the value of b is

Options

A. 0.3
B. 1.3
C. 13.2
D. 20.1

Explanation

To solve the problem, we need to find the value of \( b \) given the function \( f(x) = \log_b x \) and that \( f(2) = 0.231 \).

### Step-by-Step Solution:

1. **Write down the function**:
\[ f(x) = \log_b x \]
We are given that \( f(2) = 0.231 \).

2. **Substitute \( x = 2 \)**:
\[ f(2) = \log_b 2 = 0.231 \]

3. **Convert the logarithmic equation to exponential form**:
From the logarithmic identity, if \( \log_b a = p \), then \( a = b^p \). Here, we have:
\[ 2 = b^{0.231} \]

4. **Isolate \( b \)**:
To find \( b \), we can rewrite the equation:
\[ b^{0.231} = 2 \]

5. **Take both sides to the power of \( \frac{1}{0.231} \)**:
\[ b = 2^{\frac{1}{0.231}} \]

6. **Calculate \( 2^{\frac{1}{0.231}} \)**:
Using a calculator, we find:
\[ b \approx 20.1 \]

Thus, the value of \( b \) is approximately \( 20.1 \).

### Final Answer:
\[ b \approx 20.1 \]