Question

Resolva as equações exponenciais a seguir:

Answer 1

Olá,

a)

2^x= 64

2^x= 2⁶

x= 6

b)

5^x² - x= 25

5^x² - x= 5²

x= {-1, 2}

c)

10^1 - x= 1/10

10^1 - x= 10‐¹

x= 2

d)

(√2)^x= 4

2^x/2= 2²

x= 4

e)

(0,5)^2x= 2^1 - 3x

(1/2)^2x= 2^1 - 3x

2^-2x= 2^1 - 3x

x= 1

f)

(10^x)^1- x= 0,000001

10^x - x²= 10‐6

x= {-2, 3}

g)

(1/2)^x² - 4= 8^x + 2

2^4 - x²= 2^3x + 6

x= {-3, 0}

h)

⁵√2^x= 1/32

2^x/5= 2‐⁵

x= -25

i)

100^x + 3= 1/10

10^2x + 6= 10‐¹

x= -7/2

j)

8^x - 4= 4^x + 1

2^3x - 12= 2^2x + 2

x= 14

k)

9^x - 2= √27

3^2x - 4= 3^3/2

x= 11/4

l)

(1/16)^x - 2= 8^x

2^8 - 4x= 2^3x

x= 2

m)

(0,01)^x - 1= 1000

10^-2x + 2= 10³

x= -1/2

n)

(4^x)^x= 512²

2^2x= 2^18

x= 9

o)

(0,25)^x - 1= (1/8)^1 - x

(1/4)^x - 1= (1/8)^1 - x

2^2 - 2x= 2^3x - 3

x= 1