If log 2 = 0.3010 then log 5 equals :

Options

A. `0.3010`
B. `0.6990`
C. `0.7525`
D. Given log 2, it is not possible to calculate log 5

Answer

To find the value of log 5 given that log 2 = 0.3010, we can use the properties of logarithms.

### Step-by-Step Solution:

1. **Understand the relationship between log 5 and log 10**:
We know that:
\[ \log 5 = \log \left(\frac{10}{2}\right) \]

2. **Apply the logarithmic property**:
Using the property of logarithms that states \(\log \left(\frac{m}{n}\right) = \log m - \log n\), we can rewrite log 5:
\[ \log 5 = \log 10 - \log 2 \]

3. **Substitute the known values**:
We know that:
\[ \log 10 = 1 \quad \text{(since log base 10 of 10 is 1)} \]
and we are given that:
\[ \log 2 = 0.3010 \]
Now substituting these values into the equation:
\[ \log 5 = 1 - 0.3010 \]

4. **Perform the subtraction**:
Now, we calculate:
\[ \log 5 = 1 - 0.3010 = 0.6990 \]

5. **Final answer**:
Therefore, the value of \(\log 5\) is:
\[ \log 5 = 0.6990 \]