Step 1
Given;
[tex]5^{-x}=625[/tex]
Required; To find the solution set
Step 2
Find the solution set
[tex]using\text{ indices 625=5}^4[/tex]
Therefore, we can rewrite the equation as;
[tex]\begin{gathered} 5^{-x}=5^4 \\ Cancel\text{ the base 5 on both sides } \\ therefore;\text{ -x=4} \\ Multiply\text{ both sides by -1} \\ -x(-1)=4(-1) \\ x=-4 \end{gathered}[/tex]
Answer;
[tex]x=-4[/tex]
