Verified answer

[tex]\displaystyle 1)5^{x^2+x-12}=1\\ 5^{x^2+x-12}=5^0\\ x^2+x-12=0\\x^2+4x-3x-12=0\\x(x+4)-3(x+4)=0\\(x+4)(x-3)=0\\x+4=0,x-3=0\\x_1=-4,x_2=3\\\\2)3^{\frac{x-1}{x+1} }=9,x\neq -1 \\3^{\frac{x-1}{x+1} }=3^2 \\\\\frac{x-1}{x+1}=2\\ \\x-1=2(x+1)\\x-2x=2+1\\-x=3\\x=-3\\\\3)\frac{1}{7^{x^2-2x-3} }=1,x \in R\\\\ 1=7^{x^2-2x-3}\\ 7^{x^2-2x-3}=1\\ 7^{x^2-2x-3}=7^0\\ x^2-2x-3=0\\x^2+x-3x-3=0\\x(x+1)-3(x+1)=0\\(x+1)(x-3)=0\\x+1=0,x-3=0\\x_1=-1,x_2=3[/tex]