Question

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-halves

Answer 1

B

Explanation:

Answer 2

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.