If `log_(10)2 = 0.3010`, then `log_(2) 10` is:

Options

A. 3.01
B. 1.505
C. 3.3222
D. none of these

Answer

To find the value of \( \log_{2} 10 \) given that \( \log_{10} 2 = 0.3010 \), we can use the property of logarithms that states:

\[ \log_{a} b = \frac{1}{\log_{b} a} \]

### Step-by-Step Solution:

1. **Use the reciprocal property of logarithms**:
We know that:
\[ \log_{2} 10 = \frac{1}{\log_{10} 2} \]
This means we can find \( \log_{2} 10 \) by taking the reciprocal of \( \log_{10} 2 \).

2. **Substitute the known value**:
Given \( \log_{10} 2 = 0.3010 \), we substitute this value into the equation:
\[ \log_{2} 10 = \frac{1}{0.3010} \]

3. **Calculate the reciprocal**:
Now we need to calculate \( \frac{1}{0.3010} \):
\[ \log_{2} 10 \approx 3.32 \]
(You can use a calculator to find this value more accurately.)

4. **Final Result**:
Therefore, the value of \( \log_{2} 10 \) is approximately \( 3.32 \).