Question

Resolver em R a equação 2^2x-12.2^x+32=0

Answer 1

2^2x - 12.2^x + 32 = 0

(2^x)^2 - 12.2^x + 32 = 0

2^x = y

y^2 - 12 y + 32 = 0

a=1...b=-12...c=32

formula delta
============

D = b^2 - 4 a c

D = (-12)^2 - 4 (1) (32)

D = 144 - 4 (32)

D = 144 - 128

D = 16

formula de braskara
==================

Y = - b + , - \/D
......_________
.... ...........2 a

Y = - (-12) + , - \/16
......___________
..................2 (1)

Y = 12 + , - 4
......_______
........... ..2

Y' = 12 + 4
......._____
......... .2

Y' = 16
........__
.........2

Y' = 8

Y" = 12 - 4
........_____
.............2

Y" = 8
........__
.........2

Y" = 4


2^x = 8 ...................2^x = 4
2^x = 2^3................2^x = 2^2
x = 3.........................x = 2