Question

4^x+16=17.2^x
Equação exponencial

Answer 1

Vamos lá

4^x+16=17 • 2^x

(2²)^ x + 16 = 17 • 2^x

(2^x)² + 16= 17 • 2^x

t² + 16 = 17t

t² + 16 - 17t = 0

t² - 17t + 16 = 0

t = - ( - 17 ± √ ( - 17 ) ² - 4 • 1 • 16 / 2 • 1

t = 17 ± √ 289 - 64 / 2

t = 17 ± √ 225 / 2

t = 17 ± 15 / 2

t = 17 + 15 / 2 = 32 / 2 = 16

t = 17 - 5 / 2 = 2 / 2 = 1

t = 16

t= 1

2^x = 16
2^x = 1

2^x = 2⁴

x = 4

2^x = 1 - x = 0

x = 0

X1 = 0
X2 = 4

s { 0, 4 }