Question

Resolver estas ecuaciones exponenciales:
1) 4^(x+3) x 8^(2x-1) = √2
2) 3^(2x-1)= 1
3) 2^(3x) - 4^(x) = 8^(x+2) : 6

Answer 1

4^(x + 3) . 8^(2x - 1) = √2
2²^(x + 3) . 2³^(2x - 1) = 2¹/²
2^(2x + 6) . 2^(6x - 3) = 2¹/²
2^(2x + 6 + 6x - 3) = 2¹/²
2^(8x + 3) = 2¹/²
8x + 3 = 1/2
16x + 6 = 1
16x = - 5
x = - 5/16

3^(2x - 1) = 1
3^(2x - 1) . 3¹ = 1 . 3
3^(2x - 1 + 1) = 3¹
3^(2x) = 3¹
2x = 1
x = 1/2