we have the equation
[tex]4^{(x+3)}=7[/tex]
Solve for x
Apply log of base 4 on both sides
so
[tex]\begin{gathered} \log_44^{(x+3)}=\log_47 \\ \\ (x+3)\operatorname{\log}_44=\operatorname{\log}_47 \\ \\ (x+3)=\log_47 \\ \\ x=\log_47-3 \\ \end{gathered}[/tex]
Apply change of base
we have that
[tex]\log_47=\frac{log7}{log4}[/tex]
substitute
[tex]\begin{gathered} x=\frac{log7}{log4}-3 \\ \\ x=-1.596 \end{gathered}[/tex]
