Chapter 5 - Logarithmic Functions - 5.1 Logarithms and Their Properties - Exercises and Problems for Section 5.1 - Exercises and Problems - Page 193: 29

$x\approx3.459$

Take the log of both sides to get $$\log {2^x}=\log 11$$ Since $\log a^b=b \log a$, the expression becomes $$x \log 2 = \log 11$$ Therefore, dividing each side by $\log 2$ gives $$x=\frac{\log11}{\log 2}\approx3.459$$