If `log_10 2 = 0.3010` is given, then `log_2 10` is equal to :

Options

A. 0.301
B. 0.699
C. `(1000)/301`
D. `699/301`

Answer

To solve the problem, we need to find the value of \( \log_2 10 \) given that \( \log_{10} 2 = 0.3010 \).

### Step-by-Step Solution:

1. **Use the Change of Base Formula**:
The change of base formula for logarithms states that:
\[ \log_a b = \frac{\log_c b}{\log_c a} \]
We can use this formula to express \( \log_2 10 \) in terms of base 10 logarithms:
\[ \log_2 10 = \frac{\log_{10} 10}{\log_{10} 2} \]

2. **Evaluate \( \log_{10} 10 \)**:
The logarithm of a number to its own base is always 1:
\[ \log_{10} 10 = 1 \]

3. **Substitute the Values**:
Now we can substitute the values we have into the equation:
\[ \log_2 10 = \frac{1}{\log_{10} 2} \]
Given that \( \log_{10} 2 = 0.3010 \), we substitute this value:
\[ \log_2 10 = \frac{1}{0.3010} \]

4. **Calculate \( \frac{1}{0.3010} \)**:
To simplify \( \frac{1}{0.3010} \), we can multiply the numerator and denominator by 10000 to eliminate the decimal:
\[ \log_2 10 = \frac{10000}{3010} \]

5. **Simplify the Fraction**:
Now we can simplify \( \frac{10000}{3010} \). Dividing both the numerator and denominator by 10 gives:
\[ \log_2 10 = \frac{1000}{301} \]

### Final Answer:
Thus, the value of \( \log_2 10 \) is:
\[ \log_2 10 = \frac{1000}{301} \]