Solve for: log_{2}(x+4)-3

Expression: $\log_{ 2 }({ x+4 })-3$

Convert the constant into a logarithm with base $2$

$\log_{ 2 }({ x+4 })+\log_{ 2 }({ {2}^{-3} })$

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 $8$

$\log_{ 2 }({ \frac{ x+4 }{ 8 } })$