For what values of x does 25 Superscript x Baseline = 5 Superscript x squared minus 3? x = –3, x = 1 x = –1, x = 3 x = negative three-halves, x = 2 x = negative 2, x = three-hal…

Question

asked Dec 4, 2021 148k views

2 Answers

Lordingtar · Answer 1 · 2021-12-09T13:24:10+0000

Answer:

Option B.

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.