Answer
$x=13$
Work Step by Step
RECALL:
(i) If $a^M=a^N$, then $M=N.$
(ii) $(a^m)^n=a^{mn}.$
Write 8 and 16 as powers of 2 to obtain
$8^{x+3} = 16^{x-1}
\\(2^3)^{x+3}=(2^4)^{x-1}.$
Use rule (ii) above to obtain
$2^{3(x+3)} = 2^{4(x-1)}
\\2^{3x+9} = 2^{4x-4}.$
Use rule (i) to obtain
$3x+9=4x-4.$
Solve the equation to obtain
$9+4=4x-3x
\\13=x.$
