Respuesta :
The solutions to the problem are 2 and -5.
Given to us
[tex]12^{x^2+5x-4}= 12^{2x+6}[/tex]
To find
the value of x.
Solution
[tex]12^{x^2+5x-4}= 12^{2x+6}[/tex]
as the base on both, the sides are the same, therefore, equating the powers to each other.
[tex]{x^2+5x-4}= {2x+6}\\x^2 + 5x-2x-4-6=0\\x^2 + 5x-2x-10=0\\x(x+5)-2(x+5)=0\\(x-2)(x+5) = 0\\[/tex]
we got the two factors.
Now equating both the factors against 0,
[tex](x-2) =0\\x=2[/tex]
[tex](x+5)=0\\x=-5[/tex]
Therefore, the solutions to the problem are 2 and -5.
Learn more about factorization:
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