Question

If the characteristic of logarithm of a number is n, then the number of digits in the number is

• A. n
• B. n-1
• C. n+1
• D. n²

Answer 1

The Correct Option is C

Step 1: Recall the relationship between the characteristic of a logarithm and the number of digits.

The characteristic of the logarithm of a number gives information about the order of magnitude of the number. Specifically:

• If the characteristic of \( \log_{10}(x) \) is \( n \), then the number \( x \) lies in the range:
• A number \( x \) in this range has \( n + 1 \) digits. This is because the smallest number with \( n + 1 \) digits is \( 10^n \), and the largest number with \( n + 1 \) digits is \( 10^{n+1} - 1 \).

Step 2: Match the relationship to the options.

If the characteristic of \( \log_{10}(x) \) is \( n \), the number of digits in \( x \) is \( n + 1 \).

Final Answer: The number of digits in the number is \( \mathbf{n + 1} \), which corresponds to option \( \mathbf{(3)} \).