Jawab:
(1.)   Hp = {²log(20 - 4√21), ²log(20 + 4√21)}
(2.)  Hp = {-6, ³/₅}

Penjelasan dengan langkah-langkah:
(1.)   2²ˣ⁻¹ - 5(2ˣ⁺²) + 32 = 0
2²ˣ ÷ 2¹ - 5(2ˣ · 2²) + 32 = 0
(2ˣ)² ÷ 2¹ - 2²·5(2ˣ) + 32 = 0
(2ˣ)² ÷ 2 - 20(2ˣ) + 32 = 0
Anggap 2ˣ = u
½ u² - 20u + 32 = 0
²/₂ u² - 20u(2) + 32(2) = 0
u² - 40u + 64 = 0
u² - 40u = - 64
u² - 40u + (⁴⁰/₂)² = (⁴⁰/₂)² - 64
u² - 40u + 20² = 20² - 64
u² - 2u(20) + 20² = 400 - 64
(u - 20)² = 336
u - 20 = ±√336
u - 20 = ±√(16·21)
u - 20 = ±√16√21
u - 20 = ±4√21
u = ±4√21 + 20
2ˣ = ±4√21 + 20
2ˣ = 20 - 4√21,  2ˣ = 20 + 4√21
x = ²log(20 - 4√21),  ²log(20 + 4√21)
Hp = {²log(20 - 4√21), ²log(20 + 4√21)}
_____________________________
(2.)   (5x-2) ˣ⁻⁵ = (5x-2) ²ˣ⁺¹
x - 5 = ⁵ˣ⁻² log((5x-2) ²ˣ⁺¹)
x - 5 = (2x+1) · ⁵ˣ⁻² log(5x-2)
x - 5 = (2x+1) · 1
x - 5 = 2x+1
2x - x = -5 - 1
x = -6
Atau . .
(5x-2) ˣ⁻⁵ = (5x-2) ²ˣ⁺¹
(x-5)ln(5x-2) = (2x+1)ln(5x-2)
x ln(5x-2) - 5ln(5x-2) = 2x ln(5x-2) + ln(5x-2)
2x ln(5x-2) - x ln(5x-2) + ln(5x-2) + 5ln(5x-2) = 0
x ln(5x-2) + 6 ln(5x-2) = 0
(x + 6) ln (5x-2) = 0
x + 6 = 0,  ln (5x-2) = 0
x = -6        5x - 2 = 1
x = -6        5x = 1 + 2
x = -6        5x = 3
x = -6        x = ³/₅
Hp = {-6, ³/₅}

(xcvi)