Question

Tot fără exercițiul 48, vă rog!

Answer 1

$47) {( \frac{1}{3}) }^{2x + 5} = 3$

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

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

${3}^{ - 2x - 5} = {3}^{1}$

$- 2x - 5 = 1$

$- 2x = 1 + 5$

$- 2x = 6 \: | \div ( - 2)$

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

$49) {( \frac{1}{3}) }^{3x + 2} = 27$

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

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

${3}^{ - 3x - 2} = {3}^{3}$

$- 3x - 2 = 3$

$- 3x = 3 + 2$

$- 3x = 5 \: | \times ( - 1)$

$3x = - 5$

$x = - \frac{5}{3} \: \in \: \mathbb{R}$

$50) {( \frac{1}{5}) }^{5x - 2} = 1$

${( {5}^{ - 1}) }^{5x - 2} = {5}^{0}$

${5}^{ - 1(5x - 2)} = {5}^{0}$

${5}^{ - 5x + 2} = {5}^{0}$

$- 5x + 2 = 0$

$- 5x = - 2 \: | \times ( - 1)$

$5x = 2$

$x = \frac{2}{5} \: \in \: \mathbb{R}$

$51) {( \frac{1}{2} )}^{4x - 3} = 64$

${( {2}^{ - 1} )}^{4x - 3} = {2}^{6}$

${2}^{ - 1(4x - 3)} = {2}^{6}$

${2}^{ - 4x + 3} = {2}^{6}$

$- 4x + 3 = 6$

$- 4x = 6 - 3$

$- 4x = 3 \: | \times ( - 1)$

$4x = - 3$

$x = - \frac{3}{4} \: \in \: \mathbb{R}$