Question

Resolva as equações exponencias: 
A) 9 (elevado na x-2) = raiz de 27 
B) 5 (elevado na 2x-1) = 1
C) (2/5) (elevado na x-1) = 125/8
D) (1/2) (elevado na x)= ³raiz de 4

Answer 1

A) 9 (elevado na x-2) = √ 27 

9( elevado x -2) =27¹/²      
3²(elevado x-2)= 3³(¹/²)
2.(x-2) = 3/2
2x -4 = 3/2      mmc = 2

[4x -8= 3]/2     
4x -8= 3
4x =3 +8
x = 11/4

B) 5 (elevado na 2x-1) = 1

5(elevado 2x -1) = 5º    

2x -1 = 0
2x = +1
x = 1/2

C) (2/5) (elevado na x-1) = 125/8

(2/5)(elevado x-1) = (5/2)³

(2/5) (elevado x-1) = (2/5)⁻³

x- 1 = -3
x = -3 +1
x = -2
 

D) (1/2) (elevado na x)= ³√ 4

(1/2) elevado x = 4¹/³

(1/2) elevado x = 2²(¹/³)

(1/2) elevado x = (1/2)⁻² (¹/³)

x= -2/3

Answer 2

a)
$9^{x-2} = \sqrt{27} \\ (3^2)^{x-2} = \sqrt{3^3} \\ 3^{2x-4}= 3^{\frac{3}{2}}\\ 2x-4= \frac{3}{2} \\ \\ 2x-4= \frac{3}{2}\\ \\2x= \frac{3}{2} +4 \\ \\ 4x=11\\ x= \frac{11}{4}$

b) 
$5^{2x-1}= 1 \\ 5^{2x-1}= 5^0\\ 2x-1=0 \\ 2x= 1 \\ x= \frac{1}{2}$

c)
$( \frac{2}{5} )^{x-1}= \frac{125}{8} \\ (\frac{5}{2}^{-1})^{x-1}= (\frac{5}{2})^3 \\ \\ \frac{5}{2}^{-x+1}= (\frac{5}{2})^3 \\ \\ -x+1= 3 \\ -x= 3-1 \\ x= -2$

d)
$(\frac{1}{2})^x= \sqrt[3]{4} \\ (2^{-1})^x = \sqrt[3]{2^2} \\ 2^{-x}= 2^{\frac{2}{3}} \\ -x= \frac{2}{3} \\ \\ x= - \frac{2}{3}$