Respuesta :
For the exponential equation, having variable x as superscript equation has solution as,
[tex]x=-5,2[/tex]
What is equality for exponential equation property?
According to the equality for exponential equation property, when the bases of both side of a equation is same, then the exponents of both the terms must be equal.
The equation given in the problem is,
[tex]12^{x^2+5x-4}=12^{2x+6}[/tex]
In the given equation, the base of both side is equal. For the equal base, the exponents of them can be equate as,
[tex]{x^2+5x-4}={2x+6}[/tex]
Arrange all the terms one side of the equation as,
[tex]{x^2+5x-4}-{2x-6}=0[/tex]
Solve it further as,
[tex]{x^2+3x-10}=0[/tex]
To solve the above quadratic equation, use the split the middle term method as,
[tex]{x^2-2x+5x-10}=0\\x(x-2)+5(x-2)=0\\(x-2)(x+5)=0[/tex]
Equating both the factor to the zero, we get the value of the x as -5 and 2.
For the exponential equation, having variable x as superscript equation has solution as,
[tex]x=-5,2[/tex]
Learn more about the equality for exponential equation property here;
https://brainly.com/question/11832081
