A Rational Exponential Equation

[@RyanLewis-Johnson-wq6xs]

(25^x-16^x)/(25^x+20^x)=1/5 x=1 final answer

[@SidneiMV]

first of all divide numerator and denominator
by (5ˣ + 4ˣ)
(5ˣ - 4ˣ)/5ˣ = 1/5
1 - (4/5)ˣ = 1/5
(4/5)ˣ = 4/5 => *x = 1*

[@mystychief]

if you try x=0; x=1 then you already have it.