Question

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Answer 1

$43) {4}^{3x - 5} = 32 \times {2}^{x}$

${ ({2}^{2} )}^{3x - 5} = {2}^{5} \times {2}^{x}$

${2}^{2(3x - 5)} = {2}^{5 + x}$

${2}^{6x -10} = {2}^{5 + x}$

$6x - 10 = 5 + x$

$6x - x = 5 + 10$

$5x = 15 \: | \div 5$

$x = 3 \: \in \: \mathbb{R}$

$44) {27}^{x - 5} = 81 \times {3}^{x}$

${ ({3}^{3} )}^{x - 5} = {3}^{4} \times {3}^{x}$

${3}^{3(x - 5)} = {3}^{4 + x}$

${3}^{3x - 15} = {3}^{4 + x}$

$3x - 15 = 4 + x$

$3x - x = 4 + 15$

$2x = 19$

$x = \frac{19}{2} \: \in \: \mathbb{R}$

$45) {25}^{3x + 1} = 125 \times {5}^{x}$

${( {5}^{2}) }^{3x + 1} = {5}^{3} \times {5}^{x}$

${5}^{2(3x + 1)} = {5}^{3 + x}$

${5}^{6x + 2} = {5}^{3 + x}$

$6x + 2 = 3 + x$

$6x - x = 3 - 2$

$5x = 1$

$x = \frac{1}{5} \: \in \: \mathbb{R}$