Find the number of positive integer which have the characteristic 3 , when the base of the logarithm is 5

Options

A. 499
B. 501
C. 500
D. None of these

Explanation

To find the number of positive integers that have the characteristic 3 when the base of the logarithm is 5, we can follow these steps:

### Step 1: Understanding the Characteristic
The characteristic of a logarithm is the integer part of the logarithm value. For a logarithm with a base of 5, we want to find integers \( n \) such that:
\[ 3 \leq \log_5(n) < 4 \]

### Step 2: Converting Logarithmic Inequalities
Using the property of logarithms, we can convert the logarithmic inequalities into exponential form:
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