Question

If 142 base n is equal to 47 base ten, what is the value of base n.

Answer 1

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.