Question

Calcule as equações exponenciais pfv ajudem :)

Answer 1

Boa noite (^ - ^)

Letra A)

${64}^{x} = 256$

${(2)}^{6x} = {(2)}^{8}$

$6x = 8$

$x = \frac{8 \div 2}{6 \div 2}$

$x = \frac{4}{3}$

Letra B)

${(25)}^{x + 2} = {(125)}^{x + 5}$

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

$2(x + 2) = 3(x + 5)$

$2x + 4 = 3x + 15$

$3x - 2x = 4 - 15$

$x = - 11$

Letra C)

${( \frac{8}{125}) }^{2x - 1} = {( \frac{25}{4}) }^{2x}$

${( \frac{8}{125}) }^{2x - 1} = {( \frac{4}{25}) }^{ - 2x}$

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

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

$3(2x - 1) = - 4x$

$6x - 3 = - 4x$

$6x + 4x = 3$

$10x = 3$

$x = \frac{3}{10}$

Letra D)

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

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

$2x - 1 = 0$

$2x = 1$

$x = \frac{1}{2}$

Letra E)

${(2)}^{x + 1} + {(2)}^{x - 1} = 20$

${(2)}^{x} \times 2 + \frac{ {2}^{x} }{2} = 20$

Multiplicando tudo por 2 (Para facilitar):

${(2)}^{x} \times 4 + {2}^{x} = 40$

$5 \times {2}^{x} = 40$

${2}^{x} = 8$

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

$x = 3$

Letra F)

$\sqrt[3]{ {25}^{x} } = \sqrt{5}$

${25}^{ \frac{x}{3} } = {5}^{ \frac{1}{2} }$

${5}^{ \frac{2x}{3} } = {5}^{ \frac{1}{2} }$

$\frac{2x}{3} = \frac{1}{2}$

$2x \times 2 = 3$

$4x = 3$

$x = \frac{3}{4}$