Question

Resolva a equação exponencial
16x=28

Answer 1

$16^{x}=2^8$


Fatorar o 16:
16|2
8|2
4|2
2|2
1

$16^{x}=2^8 \\\\ (2^4)^x=2^8 \\\\ 2^4^x=2^8 \\\\ \not 2^4^x=\not 2^8 \\\\ 4x=8 \\\\ \boxed{x=2}$

Answer 2

16^x=28 =>
(2^4)^x=(2.2.7)
2^4x=2².7
Aplicando logaritmo:
Log 2^4x=Log(2².Log7)
Log 2^4x=Log 2²+Log7
Utilizando as propriedades:
4x.Log 2=2.Log 2 + Log 7
4x.0,30=2.0,30+0,85
1,20x=0,60+0,85
1,20x=1,45
x=1.45/1,20
x=1,20 aproximadamente
16^1,20=27,857618025475972452360640559352