Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 15

$x=-1$

Using exponents, the given equation, $ 2^{x+5}=16 ,$ is equivalent to \begin{array}{l}\require{cancel} 2^{x+5}=2^4 .\end{array} Since the bases are the same, the exponents can be equated. Hence, \begin{array}{l}\require{cancel} x+5=4 \\\\ x=4-5 \\\\ x=-1 .\end{array}