If (126)n=86 base 10 find the positive value of n

Answer 1

126ₙ = 86₁₀

86₁₀ = 86

126ₙ = ( 1 • n² ) + ( 2 • n¹ ) + ( 6 • n⁰ )

126ₙ = 86

( 1 • n² ) + ( 2 • n¹ ) + ( 6 • n⁰ ) = 86

n² + 2 n + 6 • 1 = 86

n² + 2 n + 6 = 86

Subtract 86 to both sides.

n² + 2 n - 80 = 0

The solutions are:

n = - 10 and n = 8

A negative number cannot be the base of a number.

- 10 cannot be the base of a number.

So n = 8

126₈ = 86₁₀