Question

Resolva as equações: a) 2^x+4 = 1/16
b) 2^x-1 + 2^x+2= 36

Answer 1

${2}^{x + 4} = \frac{1}{16}$

${2}^{x + 4} = {2}^{ \frac{1}{4} }$

$x + 4 = \frac{1}{4}$

$x = \frac{1}{4} - 4$

mmc:(1 e 4)=4

$4x = 1 - 16 \\ 4x = - 15$

$x = - \frac{15}{4}$

b)

${2}^{x - 1} + {2}^{x + 2} = 36$

${2}^{x} \times {2}^{ - 1} + {2}^{x} \times {2}^{2} = 36$

${2}^{x} \times \frac{1}{2} + {2}^{x} \times 4 = 36$

seja:

${2}^{x} = t$

vamos substituir o "t" nos lugares que tem o "x"

$\frac{1}{2} t + 4t = 36$

mmc:(2 e 1)=2

$t + 8t = 72$

$9t = 72 \\ t = \frac{72}{9}$

$t = 8$

usando:

${2}^{x} = t \: onde\\ t = 8$

${2}^{x} = 8 \\ {2}^{x} = {2}^{3}$

$x = 3$