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 that \( \log 2 = 0.3010 \) and \( \log 3 = 0.4771 \), we can use the properties of logarithms.

### Step-by-step Solution:

1. **Identify the relationship**: We know that \( 6 \) can be expressed as the product of \( 2 \) and \( 3 \):
\[ 6 = 2 \times 3 \]

2. **Apply the logarithmic property**: According to the logarithmic property, the logarithm of a product can be expressed as the sum of the logarithms:
\[ \log(6) = \log(2 \times 3) = \log(2) + \log(3) \]

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

4. **Perform the addition**:
\[ \log(6) = 0.3010 + 0.4771 = 0.7781 \]

5. **Final result**: Therefore, the value of \( \log 6 \) is:
\[ \log(6) = 0.7781 \]