Answer:
[tex] x = -\dfrac{25}{13} [/tex]
Step-by-step explanation:
[tex] \log_3{x + 4} - \log_3{x + 2} = \log_3 {27} [/tex]
[tex] \log_3 \dfrac{x + 4}{x + 2} = \log_3 {27} [/tex]
[tex] \dfrac{x + 4}{x + 2} = 27 [/tex]
[tex] x + 4 = 27(x + 2) [/tex]
[tex] x + 4 = 27x + 54 [/tex]
[tex] -26x = 50 [/tex]
[tex] x = -\dfrac{50}{26} [/tex]
[tex] x = -\dfrac{25}{13} [/tex]
