If `log_(10)2 = 0.3010` is given then `log_(2) 10` is equal to :

Options

A. 0.301
B. `0.6990`
C. `(1000)/(301)`
D. `(699)/(301)`

Answer

To find the value of \( \log_{2} 10 \) given that \( \log_{10} 2 = 0.3010 \), we can use the change of base formula for logarithms. The change of base formula states that:

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

### Step-by-Step Solution:

1. **Identify the given value**: We know that \( \log_{10} 2 = 0.3010 \).

2. **Apply the change of base formula**: We want to find \( \log_{2} 10 \). According to the change of base formula, we can express this as:
\[ \log_{2} 10 = \frac{1}{\log_{10} 2} \]

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

4. **Calculate the result**: Now we perform the division:
\[ \log_{2} 10 \approx 3.32 \]

Thus, the value of \( \log_{2} 10 \) is approximately \( 3.32 \).