Exponential inequalities and the logarithm

In an inequality aᶠ⁽ˣ⁾ > aᵍ⁽ˣ⁾ with the same base on both sides we compare the exponents. If a > 1 the function is increasing, so the sign is kept: f(x) > g(x). If 0 < a < 1 the function is decreasing, so the sign reverses: f(x) < g(x). If the bases differ we reduce them to a common base (for instance 1/2 = 2⁻¹, 8 = 2³). With several terms we take out the power with the smallest exponent or put 2ˣ = t and get a quadratic inequality, remembering that t > 0. For aˣ < b with b ≤ 0 there is no solution, and for aˣ > b with b ≤ 0 every real number is a solution, since aˣ > 0. Before writing the answer it helps to test one point.