Solve the problem,142 base (n) =47 base ten

Answer 1

To solve this problem, we need to find the value of the base, denoted as n, in which 142 in base n is equal to 47 in base ten.

Let's break down the representation of 142 base (n). In base n, the digits are multiplied by the corresponding power of n. So, in this case, it can be written as:

1 * (n^2) + 4 * (n^1) + 2 * (n^0) = 47

Simplifying the equation:

n^2 + 4n + 2 = 47

Rearranging:

n^2 + 4n - 45 = 0

Now, we need to solve this quadratic equation for n. Factoring or using the quadratic formula, we get:

(n + 9)(n - 5) = 0

This gives us two possible solutions: n = -9 or n = 5. However, since the base cannot be negative (bases are always positive), we discard n = -9.

Therefore, the solution to the problem is n = 5.