Answer:
x = - 0.55 ( 2 dec. places )
Step-by-step explanation:
Express [tex]4^{x+2}[/tex] as
[tex]4^{x}[/tex] . 4² - [tex]4^{x}[/tex] = 7
Factor out [tex]4^{x}[/tex] from each term
[tex]4^{x}[/tex] ( 4² - 1) = 7
[tex]4^{x}[/tex] × 15 = 7 ( divide both sides by 15)
[tex]4^{x}[/tex] = [tex]\frac{7}{15}[/tex]
Take the log ( base 10 ) of both sides
log [tex]4^{x}[/tex] = log ([tex]\frac{7}{15}[/tex]), thus
x log 4 = log ([tex]\frac{7}{15}[/tex] ) ( divide both sides by log 4 )
x = - 0.55
