If `log_r` 3=7.1, then `log_rsqrt3`=

Options

A. 2.66
B. 3.55
C. `(sqrt3)/r`
D. `(7.1)/r`

Explanation

To solve the problem, we need to find the value of \( \log_r \sqrt{3} \) given that \( \log_r 3 = 7.1 \).

### Step-by-Step Solution:

1. **Rewrite the logarithm of the square root**:
\[ \log_r \sqrt{3} = \log_r (3^{1/2}) \]
Here, we express the square root of 3 as \( 3^{1/2} \).

**Hint**: Remember that the square root can be expressed as a power of \( \frac{1}{2} \).

2. **Use the logarithmic property**:
According to the property of logarithms, \( \log_b (x^y) = y \cdot \log_b x \). Applying this property:
\[ \log_r \sqrt{3} = \frac{1}{2} \log_r 3 \]

**Hint**: This property allows you to bring the exponent down in front of the logarithm.

3. **Substitute the known value**:
We know from the problem statement that \( \log_r 3 = 7.1 \). Substitute this value into the equation:
\[ \log_r \sqrt{3} = \frac{1}{2} \cdot 7.1 \]

**Hint**: Always substitute known values to simplify the expression.

4. **Calculate the final result**:
Now, perform the multiplication:
\[ \log_r \sqrt{3} = \frac{7.1}{2} = 3.55 \]

**Hint**: Dividing by 2 can be done by simply halving the number.

### Final Answer:
\[ \log_r \sqrt{3} = 3.55 \]