Answer:
x=0 , x=-3
Step-by-step explanation:
Apply all exponent rules:
[tex]3^{x+3}[/tex] = [tex]3^{x}[/tex]×[tex]3^{3}[/tex]
[tex]\frac{1}{3^{x} }[/tex] = [tex](3^{x} )^{-1}[/tex]
Rewrite equation with [tex]3^{x}= u[/tex]
[tex]u[/tex] × [tex]3^{3}[/tex] + [tex]u^{-1}[/tex] - 28 = 0
Solve for u to give :
u = 1, u = 1/27
Substitute back u = [tex]3^{x}[/tex], solve for x :
[tex]3^{x}[/tex] = 1 , x= 0
[tex]3^{x}= \frac{1}{27}[/tex] , x= -3
x=0 , x=-3
Substituting x back into original equation verifies our answers
