Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 13

$x\approx3.322$

Taking the logarithm of both sides and using the properties of logarithms, the value of the variable that satisfies the given equation, $ 2^x=10 ,$ is \begin{array}{l}\require{cancel} \log2^x=\log10 \\\\ x\log2=\log10 \\\\ x=\dfrac{\log10}{\log2} \\\\ x\approx3.322 .\end{array}