Find the logarithm of the following number :
(i) 5438

Answer

To find the logarithm of the number 5438, we can break it down into simpler components. Here’s a step-by-step solution:

### Step 1: Express the number in scientific notation
We can express 5438 in scientific notation as:
\[ 5438 = 5.438 \times 10^3 \]

### Step 2: Apply the logarithm property
Using the logarithm property that states:
\[ \log(ab) = \log a + \log b \]
we can write:
\[ \log(5438) = \log(5.438 \times 10^3) \]
This can be separated into:
\[ \log(5438) = \log(5.438) + \log(10^3) \]

### Step 3: Calculate \(\log(10^3)\)
Using the property of logarithms that states:
\[ \log(10^n) = n \]
we find:
\[ \log(10^3) = 3 \]

### Step 4: Calculate \(\log(5.438)\)
To find \(\log(5.438)\), we can use a calculator or logarithm tables. The approximate value is:
\[ \log(5.438) \approx 0.735 \]

### Step 5: Combine the results
Now we can combine the results from Steps 3 and 4:
\[ \log(5438) = \log(5.438) + \log(10^3) \]
\[ \log(5438) = 0.735 + 3 \]
\[ \log(5438) \approx 3.735 \]

### Final Answer
Thus, the logarithm of 5438 is:
\[ \log(5438) \approx 3.735 \]

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