If and ( ) are the integral solutions of the equation ( _5 x )^2+ _5 ( 5 x )=1

MATHEMATICS · Numerical · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

x_1

and

x_2

(

x_2>x_1

) are the integral solutions of the equation

\left(\log_5 x\right)^2+\log_5\left(\frac{5}{x}\right)=1,

find

|x_2-4x_1|