ANSWER[tex]x = \frac{1}{2} [/tex]EXPLANATIONThe given exponential equation is [tex] {9}^{x + 1} = 27[/tex]The greatest common factor of 9 and 27 is 3. We rewrite the each side of the equation to base 3.[tex]{3}^{2(x + 1)} = {3}^{3} [/tex]Since the bases are equal, we can equate the exponents.[tex]2(x + 1) = 3[/tex]Expand the parenthesis to get:[tex]2x + 2 = 3[/tex]Group similar terms[tex]2x = 3 - 2[/tex][tex]2x = 1[/tex][tex]x = \frac{1}{2} [/tex]