Răspuns:
1.
[tex] {9}^{n + 1} = {3}^{2(n + 1)} = {3}^{2n + 2} [/tex]
[tex] {3}^{2n + 2} - {3}^{2n} \times 5 = {3}^{2n} ( {3}^{2} - 5)[/tex]
[tex] = {3}^{2n} \times 4 = {3}^{2n} \times {2}^{2} = {( {3}^{n} \times 2) }^{2} [/tex]
Care este pătrat perfect
2.
[tex] {4}^{x} = {2}^{2x} [/tex]
[tex] {8}^{x + 1} = {2}^{3x + 3} [/tex]
[tex] {4}^{x} \times {2}^{x + 2} = {2}^{2x} \times {2}^{x + 2} = {2}^{3x + 2} [/tex]
[tex] {2}^{3x} + {2}^{3x + 2} + {2}^{3x + 3} = 832[/tex]
[tex] {2}^{3x} (1 + {2}^{2} + {2}^{3} ) = 832[/tex]
[tex] {2}^{3x} \times 13 = 832[/tex]
[tex] {2}^{3x} = 64[/tex]
[tex] {2}^{6} = 64[/tex]
[tex]3x = 6[/tex]
[tex]x = 2[/tex]
