using log table evaluate `0.7625 xx 0.000357`

Answer

To evaluate \(0.7625 \times 0.000357\) using logarithms, we can follow these steps:

### Step 1: Write the expression in logarithmic form
We start by using the property of logarithms that states:
\[ \log(A \times B) = \log A + \log B \]
Here, \(A = 0.7625\) and \(B = 0.000357\).

### Step 2: Find the logarithms of the numbers
Using a logarithm table, we look up the values:
- \(\log(0.7625) \approx -0.1177676\)
- \(\log(0.000357) \approx -3.4473\)

### Step 3: Add the logarithms
Now, we can add the logarithmic values:
\[ \log(0.7625 \times 0.000357) = \log(0.7625) + \log(0.000357) \]
\[ \log(0.7625 \times 0.000357) = -0.1177676 + (-3.4473) \]
\[ \log(0.7625 \times 0.000357) = -3.5650676 \]

### Step 4: Find the antilogarithm
To find the product \(0.7625 \times 0.000357\), we need to take the antilogarithm:
\[ 0.7625 \times 0.000357 = 10^{-3.5650676} \]

### Step 5: Calculate the antilogarithm
Using the property of antilogarithm:
\[ 10^{-3.5650676} \approx 0.0002723 \]

### Final Answer
Thus, the value of \(0.7625 \times 0.000357\) is approximately \(0.0002723\).

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