Find the logarithm of the following number :
(v) 0.5438

Explanation

To find the logarithm of the number 0.5438, we can follow these steps:

### Step 1: Rewrite the number in scientific notation
We can express 0.5438 as:
\[ 0.5438 = 5.438 \times 10^{-1} \]

### Step 2: Apply the logarithm property
Using the property of logarithms that states \(\log(ab) = \log(a) + \log(b)\), we can write:
\[ \log(0.5438) = \log(5.438 \times 10^{-1}) = \log(5.438) + \log(10^{-1}) \]

### Step 3: Calculate \(\log(10^{-1})\)
We know that:
\[ \log(10^{-1}) = -1 \]

### Step 4: Find \(\log(5.438)\) using a logarithm table
From the logarithm table, we find:
\[ \log(5.438) \approx 0.735 \]

### Step 5: Combine the results
Now substituting the values we have:
\[ \log(0.5438) = \log(5.438) + \log(10^{-1}) = 0.735 - 1 \]
\[ \log(0.5438) = 0.735 - 1 = -0.265 \]

### Final Answer
Thus, the logarithm of 0.5438 is:
\[ \log(0.5438) \approx -0.265 \]

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