Question

Given that 110ₓ = 40₅ , find the value of x.

Answer 1

x = 4

Explanation:

110ₓ = 40₅ --------- change all to base ten.

the system called binary

1x²+1x ¹+0x⁰ = 45¹+0*5⁰

x² + x + 0 = 20

x² + x – 20 = 0

solve x using Quadratic equation

-1 ±
`√(1^2 - 4* 1 (-20))`

x = ------------------------------------

2 * 1

x = -5; x = 4

therefore, x = 4