If `log_(10)2= 0.3010`, then `log_(10)5`= _______

Answer

To solve the problem, we need to find the value of \( \log_{10} 5 \) given that \( \log_{10} 2 = 0.3010 \).

### Step-by-Step Solution:

1. **Understand the relationship between logarithms**:
We know that \( 5 \) can be expressed in terms of \( 10 \) and \( 2 \). Specifically, we can write:
\[ 5 = \frac{10}{2} \]

2. **Apply the logarithm property**:
Using the property of logarithms that states \( \log_b \left( \frac{A}{B} \right) = \log_b A - \log_b B \), we can rewrite \( \log_{10} 5 \) as:
\[ \log_{10} 5 = \log_{10} \left( \frac{10}{2} \right) = \log_{10} 10 - \log_{10} 2 \]

3. **Substitute known values**:
We know that \( \log_{10} 10 = 1 \) (since the logarithm of a number to its own base is 1) and we have \( \log_{10} 2 = 0.3010 \). Substituting these values gives:
\[ \log_{10} 5 = 1 - 0.3010 \]

4. **Perform the subtraction**:
Now, we calculate:
\[ 1 - 0.3010 = 0.6990 \]

5. **Final answer**:
Therefore, the value of \( \log_{10} 5 \) is:
\[ \log_{10} 5 = 0.6990 \]

### Summary:
The answer is \( \log_{10} 5 = 0.6990 \).