If n is an integer and 5^n > 40,000,000,000, what is the least possible value of n?
If n is an integer and 5^n > 40,000,000,000, what is the least possible value of n?
Answer/Solution
16
Steps/Work
When you seperate the 40000000000 into factors of 5 and 2 you get - > 10^10 x 2^2 = 5^10 x 2^12
2 to the ^ 8 = 4096 so its4096 x 5^10
that means 5^10 x 5^x must be greater
5^x > 4096
5^1=5
5^2=25
5^3= 125
5^6= 15625 - > so x must be at least 6
5^(10+6)= 5^16
A
2 to the ^ 8 = 4096 so its4096 x 5^10
that means 5^10 x 5^x must be greater
5^x > 4096
5^1=5
5^2=25
5^3= 125
5^6= 15625 - > so x must be at least 6
5^(10+6)= 5^16
A