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.