Question

Resolva as seguintes equações exponenciais:

q) 7 ˣ⁺² = 1

r) 3.2ˣ⁻² = 48

s)3.2ˣ⁺³ = 192

t) (16ˣ)ˣ⁺¹ = 0,5

Answer 1

a) ( 7 ) x + 2 = ( 7 ) 0
x+2 = 0
x = - 2

b) 3• (2) x- 2 = 48
( 2 ) x - 2 = 48 / 3
(2 ) x - 2 = 16
(2 ) x - 2 = ( 2 ) 4
x - 2 = 4
x = 4 + 2
x = 6

c) 3• (2 ) x + 3 = 192
( 2 ) x + 3 = 192 / 3
(2 ) x + 3 = 64
( 2 ) x + 3 = ( 2 ) 6
x + 3 = 6
x = 6 - 3
x = 3

d) [ ( 16) x ] x + 1 = 0,5

( 16 ) x2+ x = ( 2 ) - 1
(2 ) 4x2 + 4x = ( 2 ) - 1
4x2+4x + 1 = 0
∆ = 16 - 16
∆ = 0

x = - 4 / 8
x = - 1 / 2