Question

Me ajudem por favor, 10 pontos, foto segue abaixo, obrigado.

Answer 1

Vou respondendo devagar porque são muitas questões... Aguenta aí....

a) 2^x = 64

64 / 2
32 / 2
16 / 2
8 / 2
4 / 2
2 / 2
1

2^x = 2^6
x = 6
_______________________________

b) 3^x - 2 = 9

9 / 3
3 / 3
1

3^x - 2 = 3^2
x - 2 = 2
x = 2 + 2
x = 4
____________________________

c) 5^x² - 2x = 125

125 / 5
25 / 5
5 / 5
1

5^x² - 2x = 5^3
x² - 2x = 3
x² - 2x - 3 = 0

Delta = b² - 4ac
Delta = (-2)² - 4(1)(-3)
Delta = 4 + 12
Delta = 16

X = (-b +- raiz de Delta) / 2a
X = (2 +- 4) / 2 
x' = (2 + 4) / 2 = 6 / 2 = 3
x" = (2 - 4) / 2 = -2 / 2 = -1
___________________________________

d) 10^1 - x = 1/10
10^1 - x = 10^-1
1 - x = -1
-x = -1 - 1 (*-1)
x = 1 + 1
x = 2
____________________________________

e) (raiz de 2)^x = 4
4 / 2
2 / 2
1

(2^1/2)^x = 2²
1/2x = 2
x = 4
__________________________________

f) (0,5)^2x = (2)^1-3x
1/2^2x = (2)^1-3x
(2^-1)^2x = (2)^1-3x
-2x = 1 - 3x
-2x + 3x = 1
1x = 1
x = 1/1
x = 1
_______________________________

g) 2^4x - x² = 8

8 / 2
4 / 2
2 / 2
1

2^4x - x² = 2^3
4x - x² = 3
-x² + 4x - 3 = 0 (*-1)
x² - 4x + 3 = 0

Delta = b² - 4ac
Delta = (-4)² - 4(1)(3)
Delta = 16 - 12
Delta = 4

X = (-b +- raiz de Delta) / 2a
X = (4 +- 2) / 2
x' = (4 + 2) / 2 = 6 / 2 = 3
x" = (4 - 2) / 2 = 2 / 2 = 1

h) (10^x)^1 - x = 0.000001
(10^x)^1 - x = (10)^-6
x - x² = -6
-x² + x + 6 = 0 (*-1)
x² - x - 6 = 0

Delta = b² - 4ac
Delta = (-1)² - 4(1)(-6)
Delta = 1 + 24
Delta = 25

X = (-b +- raiz de Delta) / 2a
X = (1 +- 5) / 2
x' = (1 + 5) / 2 = 6 / 2 = 3
x" = (1 - 5) / 2 = -4 / 2 = -2
_____________________________________

i) 3^2-x = 1/27

27 / 3
9 / 3
3 / 3
1

3^2 - x = 1/3^3
3^2 - x = (3^-1)~3
2 - x = -3
-x = -3 - 2 (*-1)
x = 3 + 2
x = 5
__________________________________

j) 3^x - 5 = 27^1 - x

27 / 3
9 / 3
3 / 3
1

3^x - 5 = (3^3)^1- x
x - 5 = 3 - 3x
x + 3x = 3 + 5
4x = 8
x = 8/4
x = 2
_______________________________________

K) (1/2)^x² - 4 = 8^x + 2

8 / 2
4 / 2
2 / 2
1

(1/2)^x² - 4 = (2^3)^x + 2
(2^-1)^x² - 4 = (2^3)^x + 2
-x² + 4 = 3x + 6
-x² - 3x + 4 - 6 = 0
-x² - 3x - 2 = 0 (*-1)
x² + 3x + 2 = 0

Delta = b² - 4ac
Delta = (3)² - 4(1)(2)
Delta = 9 - 8
Delta = 1

X = (-b +- raiz de Delta) / 2a
X = (-3 +- 1) / 2
x' = (-3 + 1) / 2 = -2 / 2 = -1
x" = (-3 - 1) / 2 = -4 / 2 = -2
______________________________________

L) (raiz quinta de 2^x) = 1/32
2^x/5 = 1/(2^5)
2^x/5 = (2^-1)^5
x/5 = -5
x = -25

ESPERO TER AJUDADO!