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