Chapter 9.1, Problem 39E

Solution

To state: The smallest numbers of toppings that Luigi can offer if he claims that his selection of toppings allows for “more than 4000 different choices.”

The resultant answer is 12 toppings.

Given information:

Luigi claims that his selection of toppings allows for “more than 4000 different choices.”

Explanation:

For each pizza there are 2 choices that are include toppings or not to include it.

Let’s assume n be the smallest number of toppings that Luigi could offer. The value of n must be equal to 4000.

It can be written as:

  $2^n=4000$

Now take logarithm on both sides

  $\begin{array}{c}\log 2^n=\log 4000\\ n\log 2=\log 4000\\ n=\frac{\log 4000}{\log 2}\\ n\approx 11.97\text{or}n\approx 12\end{array}$

Therefore, the smallest number of toppings offered by Luigi is 12.