Find the number of real solutions of sin (e^x) -5^x + 5^-x

Find the number of positive integral solutions of (pairs of positive integers satisfying) x² - y² = 353702.

Solve: 2x+2^x-1+2^x-2 = 7x+7^x-1+7^x-2

Solve: (x-1)⁴+(x-5)⁴ = 82

Solve: \({ (5+2\sqrt { 6 } ) }^{ { x }^{ 2 }-3 }+{ (5-2\sqrt { 6 } ) }^{ { x }^{ 2 }-3 }=10\)