Step-by-step explanation:
[tex] {3}^{q - 7} = {27}^{q - 7} [/tex]
[tex] {3}^{q - 7} = {3}^{3(q - 7)} [/tex]
[tex]q - 7 = 3(q - 7)[/tex]
[tex]q - 7 = 3q - 21[/tex]
[tex]q - 3q = - 21 + 7[/tex]
[tex] - 2q = - 14[/tex]
[tex]q = \frac{ - 14}{ - 2} [/tex]
[tex]q = 7[/tex]
