[tex]1) {9}^{x + 2} = {3}^{ {x}^{2} + 5} [/tex]
[tex] {3}^{2(x + 2)} = {3}^{ {x}^{2} + 5} [/tex]
[tex]2(x + 2) = {x}^{2} + 5[/tex]
[tex]2x + 4 = {x}^{2} + 5[/tex]
[tex] - {x}^{2} + 2x + 4 - 5 = 0[/tex]
[tex] - {x}^{2} + 2x - 1 = 0[/tex]
[tex] {x}^{2} - 2x + 1 = 0[/tex]
[tex] {x}^{2} -x - x + 1 = 0[/tex]
[tex]x(x - 1) - (x - 1) = 0[/tex]
[tex](x - 1)(x - 1) = 0[/tex]
[tex] = > x_{1} = x_{2} = 1[/tex]
[tex]2) log_{2}(x + 2) - 1 = log_{2}(x + 1) [/tex]
[tex] log_{2}(x + 2) - log_{2}(2) = log_{2}(x + 1) [/tex]
[tex] log_{2}(\frac{x + 2}{2} ) = log_{2}(x + 1) [/tex]
[tex] \frac{x + 2}{2} = x + 1[/tex]
[tex]2(x + 1) = x + 2[/tex]
[tex]2x + 2 = x + 2[/tex]
[tex]2x - x = 2 - 2[/tex]
[tex]x = 0[/tex]
