if 100!=3^n*k what is value of n
Answers
Answer:
[100/3] + [100/9] + [100/27] + [100/81]
= 33 + 11 + 3 + 1 = 48
n is a factor of 48
Value of n = 48 if 100!=3ⁿ*k
Step-by-step explanation:
100!=3ⁿ*k
100! has numbers multiplied from 1 to 100
Factors of 3
would be
3ⁿ = 3 * 6 * 9 ...........................................................................,* 93 * 96 *, 99
=> 3ⁿ = 3³³(1 * 2 * 3 ...................................................................* 31 * 32 * 33)
Taking only 3 multiplier
=> 3ⁿ = 3³³(3 * 6..................................................................* 30 * 33)
=> 3ⁿ = 3³³ * 3¹¹ (1 * 2..................................................................* 10 * 11)
=> 3ⁿ = 3³³ * 3¹¹ (3 * 6 * 9)
=> 3ⁿ = 3⁴⁴ (3 * 6 * 9)
=> 3ⁿ = 3⁴⁴ * 3³ (1 * 2 * 3)
=> 3ⁿ = 3⁴⁷ * 3
=> 3ⁿ = 3⁴⁸
n = 8
Value of n = 48
Learn more :
Number of distinct prime factors in (729)
https://brainly.in/question/10748135
find the total number of prime factors 2^17×6^31×7^5×10^11×11^10 ...
https://brainly.in/question/10782086