If `log2=0.3010andlog3=0.4771`, find the value of
log 6

Options

A. 3
B. 0.22
C. 6
D. 0.77

Explanation

To find the value of \( \log 6 \) given \( \log 2 = 0.3010 \) and \( \log 3 = 0.4771 \), we can use the properties of logarithms.

### Step-by-step Solution:

1. **Express \( \log 6 \) in terms of \( \log 2 \) and \( \log 3 \)**:
\[ \log 6 = \log (2 \times 3) \]
Using the property of logarithms that states \( \log (a \times b) = \log a + \log b \), we can rewrite this as:
\[ \log 6 = \log 2 + \log 3 \]

2. **Substitute the known values**:
Now, we can substitute the values of \( \log 2 \) and \( \log 3 \) into the equation:
\[ \log 6 = 0.3010 + 0.4771 \]

3. **Perform the addition**:
Adding the two values together:
\[ \log 6 = 0.3010 + 0.4771 = 0.7781 \]

4. **Final result**:
Thus, the value of \( \log 6 \) is:
\[ \log 6 \approx 0.7781 \]
This can be rounded to \( 0.77 \).

### Conclusion:
The value of \( \log 6 \) is approximately \( 0.77 \).