Find the number of positive integer which have the characteristic 3 , when the base of the logarithm is 5
A
499
B
501
C
500
D
None of these
Text Solution
AI Generated Solution
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:
...
Topper's Solved these Questions
CONTINUITY AND DIFFERENTIABILITY
NCERT|Exercise EXERCISE 5.7|17 Videos
APPLICATION OF INTEGRALS
NCERT|Exercise EXERCISE 8.2|7 Videos
DETERMINANTS
NCERT|Exercise EXERCISE 4.4|5 Videos
Similar Questions
Explore conceptually related problems
Find the number of positive integers which have the characterstics 3 when the base of the logarithm is 7
Let S denotes the antilog of 0.5 to the base 256 and K denotes the number of digits in 6^(10) (given log_(10)2=0.301 , log_(10)3=0.477 ) and G denotes the number of positive integers, which have the characteristic 2, when the base of logarithm is 3. The value of SKG is
Let 'L' denotes the antilog of 0.4 to the base 1024. and 'M' denotes the number of digits in 6^(10) (Given log,02-03 and 'N' denotes the number of positive integers which have the characteristic 2, when base of the logarithm is 6. Find the value of LMN
Let L denote antilog 320.6 and M denote the number of positive integers which have the characteristic 4, when the base of log is 5, and N denote the value of 49^((1-log_(7)2))+5^(-log_(5)4) Find the value of (LM)/(N) .
Find the number of even positive number which have five digits.
How many positive integers have characteristics 2 when base is 5.
Find the number of even positive numbers which have four digits.
The characteristic of the logarithm of 3.6275 is ______.
Find the number of odd positive three digit integers.
Find the number of all positive integers of 3 digits which are divisibleby 5.
Knowledge Check
Let S denotes the antilog of 0.5 to the base 256 and K denotes the number of digits in 6^(10) (given log_(10)2=0.301 , log_(10)3=0.477 ) and G denotes the number of positive integers, which have the characteristic 2, when the base of logarithm is 3. The value of SKG is
