Question

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

Answer 1

Answer:

x = 4

Step-by-step 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 ± $\sqrt{1^2 - 4* 1 (-20)}$

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

                        2 * 1

x = -5;  x = 4

therefore, x = 4