Respuesta :
8^x+3=16^x+1, 2^3(x+3)=2^4(x+1), 2^3x+9=2^4x+4, same bases. 3x+9=4x+4, 3x-4x=4-9, -x=-5, x=5
[tex]\bf 8^{x+3}=16^{x-1}\qquad
\begin{cases}
8=2\cdot 2\cdot 2\\
\qquad 2^3\\
16=2\cdot 2\cdot 2\cdot 2\\
\qquad 2^4
\end{cases}\implies (2^3)^{x+3}=(2^4)^{x-1}
\\\\\\
2^{3(x+3)}=2^{4(x-1)}\impliedby
\begin{array}{llll}
\textit{since the bases are the same}\\
\textit{the exponents must also be the same}
\end{array}
\\\\\\
3(x+3)=4(x-1)\implies 3x+9=4x-4\implies 9+4=4x-3x
\\\\\\
\boxed{13=x}[/tex]
