A nice math olympiad question || you should know this trick ||

[@oahuhawaii2141]

2ˣ + x = 1034 2ˣ = 1034 - x LHS: Power curve from above the asymptote of 0 for x < 0 , climbs to 1 at x = 0 , and goes unbounded for x > 0 . RHS: Line sloping down from (0, 1034) to (1034, 0) . They intersect only once. 2¹⁰ = 1034 - 10 1024 = 1024 x = 10