Chapter 4.5, Problem 68E

To determine

Solve the inequality.

Answer to Problem 68E

  $\boxed{8\le x\le 16}$

Explanation of Solution

Given information:

Solve the inequality.

  $3\le {\log }_{2}x\le 4$

Calculation:

Consider the given inequality,

  $3\le {\log }_{2}x\le 4$

Take $3\le {\log }_{2}x$ ,

  $\begin{array}{l}{2}^3\le x\\ 8\le x\mathrm{.......}\left(1\right)\\ now,take\\ {\log }_{2}x\le 4\\ 2^4\le x\\ 16\le x\mathrm{......}\left(2\right)\\ from\left(1\right)and\left(2\right)\\ 8\le x\le 16\end{array}$

Hence, the solution is, $\boxed{8\le x\le 16}$