Question

For what values of x does 25 Superscript x Baseline = 5 Superscript x squared minus 3?

Answer 1

Answer:

Option B.

Step-by-step explanation:

The given equation is

$25^x=5^{x^2-3}$

It can be rewritten as

$(5^2)^x=5^{x^2-3}$

$5^{2x}=5^{x^2-3}$

On comparing both sides, we get

$2x=x^2-3$

$0=x^2-2x-3$

Now,

$x^2-3x+x-3=0$

$x(x-3)+(x-3)=0$

$(x-3)(x+1)=0$

Using zero f=product property, we get

$x-3=0\Rightarrow x=3$

$x+1=0\Rightarrow x=-1$

Therefore, the correct option is B.