Question

Questão de matemática 1 até o 4

Answer 1

1) a -

${2}^{ x + 3 } = 512$
${2}^{x + 3} = {2}^{9}$
x + 3 = 9

x = 9 - 3

x = 6

b -
$\sqrt[3]{81} = {3}^{x + 1}$
${3}^{ \frac{4}{3} } = {3}^{x + 1}$
4/3 = x + 1

4 = 3x + 3

3x = 1

x = 1/3

2)
${2}^{x + 3} + {2}^{x - 1} = 17$
${2}^{x} . {2}^{3} + {2}^{x} . {2}^{ - 1} = 17$
$8. {2}^{x} + \frac{1}{2} . {2}^{x} = 17$
$16 .{2}^{x} + {2}^{x} = 34$
${2}^{x} .(16 + 1) = 34$
${2}^{x} = \frac{34}{17}$
${2}^{x} = 2$

x = 1

3)
${2}^{4x + 1} . {8}^{ - x + 3} = {16}^{ - 1}$
${2}^{4x + 1} . {2}^{ - 3x + 9 } = {2}^{ - 4}$

4x +1 - 3x + 9 = -4

x = - 14

4)
$( { \frac{5}{2} })^{x} = ({ \frac{25}{4} })^{ x + 2}$
$( { \frac{5}{2} })^{x} = ({ \frac{5}{2} })^{2x + 4}$

x = 2x + 4

x = - 4

D