Explicație pas cu pas:
[tex]a) {9}^{x - 3} = {9}^{5} \\ \\ {(3}^{2})^{x - 3} = {(3}^{2})^{5} \\ \\ {3}^{2(x - 3)} = {3}^{2 \times 5} \\ \\ {3}^{2(x - 3)} = {3}^{10} \\ \\ 2(x - 3) = 10 \\ \\ 2x - 2 \times 3 = 10 \\ \\ 2x - 6 = 10 \\ \\ (2x - 6) + 6 = 10 + 6 \\ \\ 2x - 6 + 6 = 16 \\ \\ 2x = 16 \\ \\ \frac{2x}{2} = \frac{16}{2} \\ \\ x = 8 [/tex]
[tex]b) {3}^{x} = 27 \\ \\ {3}^{x} = {3}^{3} \\ \\ x = 3 [/tex]
[tex]c) {2}^{x - 3} = 4 \\ \\ {2}^{x - 3} = {2}^{2} \\ \\ x - 3 = 2 \\ \\ (x - 3) + 3 = 2 + 3 \\ \\ x - 3 + 3 = 5 \\ \\ x = 5 [/tex]
[tex]d) {3}^{2x + 2} = 9 \\ \\ {3}^{2x + 2} = {3}^{2} \\ \\ 2x + 2 = 2 \\ \\ 2x = 0 \\ \\ \frac{2x}{2} = 0 \\ \\ x = 0 [/tex]
[tex]e) \sqrt{x} = 7 \\ \\ \sqrt{x}^{2} = {7}^{2} \\ \\ x = 49 [/tex]
[tex]f) \sqrt{1 + 3x} = 4 \\ \\ \sqrt{3x + 1} = 4 \\ \\ {( \sqrt{3x + 1}) }^{2} = {4}^{2} \\ \\ \sqrt{ {(3x + 1)}^{2} } = 16 \\ \\ {(3x + 1})^{ \frac{2}{2} } = 16 \\ \\ 3x + 1 = 16 \\ \\ (3x + 1) + ( - 1) = 16 + ( - 1) \\ \\ 3x + 1 - 1 = 16 - 1 \\ \\ 3x = 15 \\ \\ \frac{3x}{3} = \frac{15}{3} \\ \\ x = 5 [/tex]
