Solve the problem 132 base (n)=72 base ten

1 answer

To solve this problem, we need to find the value of n.

In base n, the number 132 is equal to 1*n^2 + 3*n^1 + 2*n^0.

In base ten, the number 72 is equal to 7*10^1 + 2*10^0.

Setting these two expressions equal, we get:

1*n^2 + 3*n^1 + 2*n^0 = 7*10^1 + 2*10^0

Re-arranging the equation, we have:

1*n^2 + 3*n - 68 = 0

To solve for n, we can use the quadratic formula:

n = (-3 ± √(3^2 - 4*1*(-68))) / (2*1)

n = (-3 ± √(9 + 272)) / 2

n = (-3 ± √281) / 2

Therefore, the value of n is approximately -9.36 or 6.36, since n cannot be negative in this case.