To solve for x:
[tex]15=5^{x+3}-7[/tex]
On simplification we get,
[tex]\begin{gathered} 15+7=5^{x+3} \\ 22=5^{x+3} \\ 5^{x+3}=22 \end{gathered}[/tex]
Taking log base 5 on both sides, we get,
[tex]\begin{gathered} x+3=\log _522 \\ x+3=1.92057 \\ x=1.92057-3 \\ x=-1.07943 \end{gathered}[/tex]
Hence, the value of x is -1.079 (Rounded to the nearest thousandth).
Therefore, the correct option is C.
