Question

If 2(log x)^2+5(log x)-18=0 then what is the value of x?

Answer 1

Let log x = y

We substitute this into the equation as follows :

2y² + 5y - 18 =0

This is a quadratic equation hence we solve it.

The roots are +9 and - 4

Doing the substitution we have :

(2y + 9)(y - 2) = 0

2y = - 9

y = - 4.5

Y = 2

Log x is thus equal to = 2 or - 4.5

To get x, we get the antilog of 2 and - 4.5

Antilog of 2= 100

Antilog of - 4.5 =3.16228 × 10⁻⁵

The value of x is thus 100 or 3.16228 × 10⁻⁵