Find the logarithm of the following number :
(vi) 0.05438

Explanation

To find the logarithm of the number 0.05438, we can follow these steps:

### Step 1: Express the Number in Scientific Notation
We start by expressing 0.05438 in scientific notation:
\[ 0.05438 = 5.438 \times 10^{-2} \]

### Step 2: Use the Logarithmic Property
Next, we apply the logarithmic property that states:
\[ \log(a \times b) = \log(a) + \log(b) \]
Thus, we can write:
\[ \log(0.05438) = \log(5.438 \times 10^{-2}) = \log(5.438) + \log(10^{-2}) \]

### Step 3: Calculate \(\log(10^{-2})\)
Using the logarithmic identity \(\log(10^n) = n\), we find:
\[ \log(10^{-2}) = -2 \]

### Step 4: Find \(\log(5.438)\)
Now, we need to find \(\log(5.438)\). We can refer to a logarithm table or use a calculator for this value. Assuming we find:
\[ \log(5.438) \approx 0.735 \]

### Step 5: Combine the Results
Now we can combine our results from Steps 3 and 4:
\[ \log(0.05438) = \log(5.438) + \log(10^{-2}) = 0.735 - 2 \]

### Step 6: Final Calculation
Finally, we perform the calculation:
\[ 0.735 - 2 = -1.265 \]

Thus, the logarithm of 0.05438 is:
\[ \log(0.05438) \approx -1.265 \]

### Summary
The logarithm of 0.05438 is approximately -1.265.

---