[tex]47) {( \frac{1}{3}) }^{2x + 5} = 3[/tex]
[tex] {( {3}^{ - 1}) }^{2x + 5} = {3}^{1} [/tex]
[tex] {3}^{ - 1(2x + 5)} = {3}^{1} [/tex]
[tex] {3}^{ - 2x - 5} = {3}^{1} [/tex]
[tex] - 2x - 5 = 1[/tex]
[tex] - 2x = 1 + 5[/tex]
[tex] - 2x = 6 \: | \div ( - 2)[/tex]
[tex]x = - 3 \: \in \: \mathbb{R}[/tex]
[tex]49) {( \frac{1}{3}) }^{3x + 2} = 27[/tex]
[tex] { ({3}^{ - 1} )}^{3x + 2} = {3}^{3} [/tex]
[tex] {3}^{ - 1(3x + 2)} = {3}^{3} [/tex]
[tex] {3}^{ - 3x - 2} = {3}^{3} [/tex]
[tex] - 3x - 2 = 3[/tex]
[tex] - 3x = 3 + 2[/tex]
[tex] - 3x = 5 \: | \times ( - 1)[/tex]
[tex]3x = - 5[/tex]
[tex]x = - \frac{5}{3} \: \in \: \mathbb{R}[/tex]
[tex]50) {( \frac{1}{5}) }^{5x - 2} = 1[/tex]
[tex] {( {5}^{ - 1}) }^{5x - 2} = {5}^{0} [/tex]
[tex] {5}^{ - 1(5x - 2)} = {5}^{0} [/tex]
[tex] {5}^{ - 5x + 2} = {5}^{0} [/tex]
[tex] - 5x + 2 = 0[/tex]
[tex] - 5x = - 2 \: | \times ( - 1)[/tex]
[tex]5x = 2[/tex]
[tex]x = \frac{2}{5} \: \in \: \mathbb{R}[/tex]
[tex]51) {( \frac{1}{2} )}^{4x - 3} = 64[/tex]
[tex] {( {2}^{ - 1} )}^{4x - 3} = {2}^{6} [/tex]
[tex] {2}^{ - 1(4x - 3)} = {2}^{6} [/tex]
[tex] {2}^{ - 4x + 3} = {2}^{6} [/tex]
[tex] - 4x + 3 = 6[/tex]
[tex] - 4x = 6 - 3[/tex]
[tex] - 4x = 3 \: | \times ( - 1)[/tex]
[tex]4x = - 3[/tex]
[tex]x = - \frac{3}{4} \: \in \: \mathbb{R}[/tex]
