The mantissa of `log 3274` is `0.5150` then the value of ` log32.74 ` is______

Options

A. 1.515
B. 2.515
C. 0.515
D. `bar1`.515

Answer

To find the value of \( \log 32.74 \) given that the mantissa of \( \log 3274 \) is \( 0.5150 \), we can follow these steps:

### Step 1: Understand the relationship between \( \log 3274 \) and \( \log 32.74 \)

We know that:
\[ \log 3274 = \log(32.74 \times 100) = \log 32.74 + \log 100 \]

### Step 2: Use the property of logarithms

From the properties of logarithms, we have:
\[ \log 100 = \log(10^2) = 2 \log 10 = 2 \]
since \( \log 10 = 1 \).

### Step 3: Substitute the known values

Now, we can substitute this back into our equation:
\[ \log 3274 = \log 32.74 + 2 \]

### Step 4: Rearrange to find \( \log 32.74 \)

Rearranging the equation gives us:
\[ \log 32.74 = \log 3274 - 2 \]

### Step 5: Find \( \log 3274 \)

We know that the mantissa of \( \log 3274 \) is \( 0.5150 \). Therefore, we can express \( \log 3274 \) as:
\[ \log 3274 = 3 + 0.5150 = 3.5150 \]

### Step 6: Substitute \( \log 3274 \) into the equation

Now we can substitute this value into our rearranged equation:
\[ \log 32.74 = 3.5150 - 2 \]

### Step 7: Calculate \( \log 32.74 \)

Calculating this gives:
\[ \log 32.74 = 1.5150 \]

### Final Answer

Thus, the value of \( \log 32.74 \) is:
\[ \boxed{1.5150} \]

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