College Algebra, Chapter 10, Review Exercises, Section Review Exercises, Problem 14

A pizza parlor advertises that they prepare 2048 different types of pizza. How many toppings does this parlor offer?

We need the number of possible subsets of the $n$ toppings. Thus, $2^n = 2048$


$\begin{equation} \begin{aligned} 2^n =& 2048 && \\ \ln 2^n =& \ln 2048 && \text{Take $\ln$ of both sides} \\ \\ n \ln 2 =& \ln 2048 && \text{Property of } \ln \\ \\ n =& \frac{\ln 2048}{\ln 2} && \text{Divide by } \ln 2 \\ \\ n =& 11 && \end{aligned} \end{equation}$


The pizza parlor has 11 different toppings to offer.