Find the logarithm of the following number :
(iv) 5.438

Answer

To find the logarithm of the number 5.438, we can follow these steps:

### Step 1: Identify the number and its parts
We need to find the logarithm of 5.438. This number can be broken down into its whole number and decimal parts. The whole number part is 5, and the decimal part is 0.438.

### Step 2: Use a logarithmic table
To find the logarithm, we can use a logarithmic table. This table provides the logarithmic values for various numbers. We will first look for the logarithm of the whole number part, which is 5.4.

### Step 3: Locate the logarithm of 5.4
In the logarithmic table, we find the row for 5.4. The logarithm of 5.4 is approximately 0.732.

### Step 4: Determine the second decimal place
Next, we need to consider the second decimal place of our number, which is 3 (from 5.43). We will look at the logarithmic table for the value corresponding to 0.03 (the second decimal).

### Step 5: Find the intersection value
In the logarithmic table, we find the intersection of the row for 5.4 and the column for 0.03. This intersection gives us an additional value that we need to add to the logarithm of 5.4. The value at this intersection is approximately 0.735.

### Step 6: Combine the values
Since we are only interested in the first two decimal places, we can take the logarithm value of 5.4 (which is 0.732) and add the value from the intersection (which is approximately 0.003). Therefore, the logarithm of 5.438 can be approximated as:

\[ \log(5.438) \approx 0.732 + 0.003 = 0.735 \]

### Final Answer
Thus, the logarithm of 5.438 is approximately **0.735**.

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