[tex]43) {4}^{3x - 5} = 32 \times {2}^{x} [/tex]
[tex] { ({2}^{2} )}^{3x - 5} = {2}^{5} \times {2}^{x} [/tex]
[tex] {2}^{2(3x - 5)} = {2}^{5 + x} [/tex]
[tex] {2}^{6x -10} = {2}^{5 + x} [/tex]
[tex]6x - 10 = 5 + x[/tex]
[tex]6x - x = 5 + 10[/tex]
[tex]5x = 15 \: | \div 5[/tex]
[tex]x = 3 \: \in \: \mathbb{R}[/tex]
[tex]44) {27}^{x - 5} = 81 \times {3}^{x} [/tex]
[tex] { ({3}^{3} )}^{x - 5} = {3}^{4} \times {3}^{x} [/tex]
[tex] {3}^{3(x - 5)} = {3}^{4 + x} [/tex]
[tex] {3}^{3x - 15} = {3}^{4 + x} [/tex]
[tex]3x - 15 = 4 + x[/tex]
[tex]3x - x = 4 + 15[/tex]
[tex]2x = 19[/tex]
[tex]x = \frac{19}{2} \: \in \: \mathbb{R}[/tex]
[tex]45) {25}^{3x + 1} = 125 \times {5}^{x} [/tex]
[tex] {( {5}^{2}) }^{3x + 1} = {5}^{3} \times {5}^{x} [/tex]
[tex] {5}^{2(3x + 1)} = {5}^{3 + x} [/tex]
[tex] {5}^{6x + 2} = {5}^{3 + x} [/tex]
[tex]6x + 2 = 3 + x[/tex]
[tex]6x - x = 3 - 2[/tex]
[tex]5x = 1[/tex]
[tex]x = \frac{1}{5} \: \in \: \mathbb{R}[/tex]
