Answer:
Option B.
Step-by-step explanation:
The given equation is
[tex]25^x=5^{x^2-3}[/tex]
It can be rewritten as
[tex](5^2)^x=5^{x^2-3}[/tex]
[tex]5^{2x}=5^{x^2-3}[/tex]
On comparing both sides, we get
[tex]2x=x^2-3[/tex]
[tex]0=x^2-2x-3[/tex]
Now,
[tex]x^2-3x+x-3=0[/tex]
[tex]x(x-3)+(x-3)=0[/tex]
[tex](x-3)(x+1)=0[/tex]
Using zero f=product property, we get
[tex]x-3=0\Rightarrow x=3[/tex]
[tex]x+1=0\Rightarrow x=-1[/tex]
Therefore, the correct option is B.
