The mantissa of log 3274 is 0.5150. The value of `log(0.3274)` is:

Options

A. `bar(1).5150`
B. 1.515
C. `bar(2).5150`
D. none of these

Answer

To find the value of \( \log(0.3274) \) given that the mantissa of \( \log(3274) \) is \( 0.5150 \), we can follow these steps:

### Step 1: Understand the relationship between logarithms of numbers and their decimal counterparts
We know that:
\[ \log(0.3274) = \log\left(\frac{3274}{10000}\right) = \log(3274) - \log(10000) \]
Since \( \log(10000) = 4 \) (because \( 10000 = 10^4 \)), we can rewrite the equation as:
\[ \log(0.3274) = \log(3274) - 4 \]

### Step 2: Substitute the value of \( \log(3274) \)
From the problem, we know that:
\[ \log(3274) = 3 + 0.5150 = 3.5150 \]
Now we substitute this value into our equation:
\[ \log(0.3274) = 3.5150 - 4 \]

### Step 3: Calculate the result
Now we perform the subtraction:
\[ \log(0.3274) = 3.5150 - 4 = -0.4850 \]

### Step 4: Express the result in standard logarithmic form
In standard logarithmic form, we express negative values with a bar:
\[ \log(0.3274) = -1 + 0.5150 = 1\overline{0.5150} \]

### Final Answer
Thus, the value of \( \log(0.3274) \) is:
\[ \boxed{1\overline{0.5150}} \]

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