Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 14

$x\approx4.585$

Taking the logarithm of both sides and using the properties of logarithms, the value of the variable that satisfies the given equation, $ 2^x=24 ,$ is \begin{array}{l}\require{cancel} \log2^x=\log24 \\\\ x\log2=\log24 \\\\ x=\dfrac{\log24}{\log2} \\\\ x\approx4.585 .\end{array}