$\log_{ 2 }({ x+4 })+\log_{ 2 }({ {2}^{-3} })$
Use $\log_{ a }({ x })+\log_{ a }({ y })=\log_{ a }({ x \times y })$ to simplify the expression$\log_{ 2 }({ \left( x+4 \right) \times {2}^{-3} })$
Express with a positive exponent using ${a}^{-n}=\frac{ 1 }{ {a}^{n} }$$\log_{ 2 }({ \left( x+4 \right) \times \frac{ 1 }{ {2}^{3} } })$
Evaluate the power$\log_{ 2 }({ \left( x+4 \right) \times \frac{ 1 }{ 8 } })$
Distribute $\frac{ 1 }{ 8 }$ through the parentheses$\log_{ 2 }({ \frac{ 1 }{ 8 }x+\frac{ 1 }{ 2 } })$
Write all numerators above the least common denominator $8$$\log_{ 2 }({ \frac{ x+4 }{ 8 } })$