Chapter 1.7, Problem 37E

To determine

To select: the expression from the given options that is not larger than $5\times 6^{12}$ .

Answer to Problem 37E

  $\text{A}\text{. }5+6^{12}$

Explanation of Solution

Given information:

The given options are as follows:

  $\begin{array}{l}\text{A}\text{. }5+6^{12}\\ \text{B}\text{. }7\times 6^{12}\\ \text{C}\text{. }5\times 8^{12}\\ \text{D}\text{. }5\times 6^{14}\\ \text{E}\text{. }{10}^{13}\end{array}$

Calculation:

Compare $5+6^{12}$ with $5\times 6^{12}$ as shown below.

  $\begin{array}{l}5+6^{12}\text{ vs }5\times 6^{12}\\ 5+6^{12}<5\times 6^{12}\left[\text{It is like a billion and 5 vs 5 billion}\right]\end{array}$

Compare $7\times 6^{12}$ with $5\times 6^{12}$ as shown below.

  $\begin{array}{l}7\times 6^{12}\text{ vs }5\times 6^{12}\\ 7>5\left[{\text{Dividing both sides by 6}}^{12}\text{ and comparing the values}\right]\\ \therefore 7\times 6^{12}\text{ > }5\times 6^{12}\end{array}$

Compare $5\times 8^{12}$ with $5\times 6^{12}$ as shown below.

  $\begin{array}{l}5\times 8^{12}\text{ vs }5\times 6^{12}\\ 8^{12}>6^{12}\left[\text{Dividing both sides by 5 and comparing the values}\right]\\ \therefore 5\times 8^{12}\text{ > }5\times 6^{12}\end{array}$

Compare $5\times 6^{14}$ with $5\times 6^{12}$ as shown below.

  $\begin{array}{l}5\times 6^{14}\text{ vs }5\times 6^{12}\\ 6^2>1\left[\text{Dividing both sides by }5\times 6^{12}\text{ and comparing the values}\right]\\ \therefore 5\times 6^{14}\text{ > }5\times 6^{12}\end{array}$

Compare ${10}^{13}$ with $5\times 6^{12}$ as shown below.

  $\begin{array}{l}{10}^{13}\text{ vs }5\times 6^{12}\\ 10,000,000,000,000>10,883,911,680\left[\text{Solve both the values}\right]\\ \therefore {10}^{13}\text{ > }5\times 6^{12}\end{array}$

Since the expression $5+6^{12}$ is not larger than $5\times 6^{12}$ . So, option A is correct.