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[@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