4)
a) 9^x = 729
(3²)^x = 2 × 243 = 3 × 3 x 81 = 3² x 9² = 3² × (3²)² = 3² x 3^4 = 3^6
2x = 6
x = 3
b) 25^(x + 1) = 125² = (5 × 25)² = (5 × 5²)²= (5³)² = 5^6
(5²)^(x + 1) = 5^6
2(x + 1) = 6
2x + 2 = 6
2x = 4
x = 2
c) 11^(3x + 2) = 121^4 = (11²)^4 = 11^8
3x + 2 = 8
3x = 6
x = 2
d) 216^(x - 3) = (6^7)^3 = 6^21
(6 × 6²)(x - 3) = 6^21
6^3(x - 3) = 6^21
3x - 9 = 21
3x = 21 - 9 = 12
x = 4
5)
a) x³ + 1 = 217
x³ = 216 = 2 × 108 = 2 × 2 × 54 = 2 × 2 × 2 ×27 = 2³ × 3 × 9 = 2³ × 3³ = (2 × 3)³
x = 2 × 3 = 6
b) (x - 2)^4 = 81 = 9 × 9 = 3² × 3² = 3^4
x - 2 = 3
x = 5
c) (2x + 1)^14 = 25^7 = (5²)^7 = 5^14
2x + 1 = 5
2x = 4
x = 2
d) (3x + 1)^24 = (10³)^8 = 10^24
3x + 1 = 10
3x = 9
x = 3
