Question

va roooog am nevooooie de ajutooor
ex 29.

Answer 1

$a) {2}^{x + 5} = 64 \\ \\ {2}^{x + 5} = {2}^{6} \\ \\ x + 5 = 6 \\ \\ x = 6 - 5 = 1$

$b) {3}^{x - 12} = 27 \\ \\ {3}^{x - 12} = {3}^{3} \\ \\ x - 12 = 3 \\ \\ x = 3 + 12 = 15$

$c) {4}^{x - 4} = 16 \\ \\ {4}^{x - 4} = {4}^{2} \\ \\ x - 4 = 2 \\ \\ x = 2 + 4 = 6$

$d) {5}^{x - 7} = 125 \\ \\ {5}^{x - 7} = {5}^{3} \\ \\ x - 7 = 3 \\ \\ x = 3 + 7 = 10$

$e) {2}^{3x - 6} = 8 \\ \\ {2}^{3x - 6} = {2}^{3} \\ \\ 3x - 6 = 3 \\ \\ 3x = 3 + 6 = 9 \\ \\ = > x = 3$

$f) {3}^{5x - 12} = 27 \\ \\ {3}^{5x - 12} = {3}^{3} \\ \\ 5x - 12 = 3 \\ \\ 5x = 3 + 12 = 15 \\ \\ = > x = 3$

$g) {2}^{x} + {2}^{x + 1} = 12 \\ \\ (1 + 2) \times {2}^{x} = 12 \\ \\ 3 \times {2}^{x} = 12 \\ \\ {2}^{x} = 4 \\ \\ {2}^{x} = {2}^{2} \\ \\ = > x = 2$

$h) {3}^{x} + {3}^{x + 1} = 36 \\ \\ (1 + 3) \times {3}^{x} = 36 \\ \\ 4 \times {3}^{x} = 36 \\ \\ {3}^{x} = 9 \\ \\ {3}^{x} = {3}^{2} \\ \\ = > x = 2$