Question
If 142 base n is equal to 47 base ten, what is the value of base n.
Answers
GPT 3.5
To solve this problem, we need to find the value of base n.
We are given that 142 base n is equal to 47 base ten.
Let's convert 142 base n to base ten:
142 base n = 1*n^2 + 4*n^1 + 2*n^0
Using the expanded form, we can express this equation as:
142 base n = n^2 + 4n + 2
Now, we can set this equation equal to 47 base ten:
n^2 + 4n + 2 = 47
Rearranging the equation:
n^2 + 4n + 2 - 47 = 0
n^2 + 4n - 45 = 0
Now, we can factor this equation:
(n + 9)(n - 5) = 0
Setting each factor equal to zero:
n + 9 = 0 or n - 5 = 0
n = -9 or n = 5
Since the base cannot be negative, the value of base n is 5.
We are given that 142 base n is equal to 47 base ten.
Let's convert 142 base n to base ten:
142 base n = 1*n^2 + 4*n^1 + 2*n^0
Using the expanded form, we can express this equation as:
142 base n = n^2 + 4n + 2
Now, we can set this equation equal to 47 base ten:
n^2 + 4n + 2 = 47
Rearranging the equation:
n^2 + 4n + 2 - 47 = 0
n^2 + 4n - 45 = 0
Now, we can factor this equation:
(n + 9)(n - 5) = 0
Setting each factor equal to zero:
n + 9 = 0 or n - 5 = 0
n = -9 or n = 5
Since the base cannot be negative, the value of base n is 5.