Solve for x. 3^x−1=9^x+2 Enter your answer in the box. x =

The solution is x = -5Step-by-step explanation:Given equation is:[tex]3^{(x-1)} = 9^{(x+2)}[/tex]In order to solve the eponnetial equations, we have to equate the bases of both sides so that the exponents can be put equalSo,Replacing 9 with 3^2[tex]3^{(x-1)} = (3^2)^{(x+2)}[/tex]When there are exponents on exponents, both are multiplied so,[tex]3^{(x-1)} = 3^{(2x+4)}[/tex]As the bases on both sides are same, the exponents can be put equalSo,[tex]x-1 = 2x+4[/tex]Adding 1 on both sides[tex]x-1+1 = 2x+4+1\\x = 2x+5[/tex]Subtracting 2x from both sides[tex]x-2x = 2x-2x+5\\-x = 5\\x = -5[/tex]Hence,The solution is x = -5Keywords: Exponents, EquationsLearn more about exponential equations at:brainly.com/question/1993757brainly.com/question/2115122#LearnwithBrainly