Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - 12.3 Logarithmic Functions - 12.3 Exercise Set - Page 803: 40

Answer

The graph is shown below.

Work Step by Step

$y={{\log }_{2}}x$ The function $y={{\log }_{2}}x$ can be written as $x={{2}^{y}}$. Substitute $y=0$ in $x={{2}^{y}}$: $\begin{align} & x={{2}^{0}} \\ & =1 \end{align}$ Substitute $y=1$ in $x={{2}^{y}}$: $\begin{align} & x={{2}^{1}} \\ & =2 \end{align}$ Substitute $y=2$ in $x={{2}^{y}}$: $\begin{align} & x={{2}^{2}} \\ & =4 \end{align}$ Substitute $y=-1$ in $x={{2}^{y}}$: $\begin{align} & x={{2}^{-1}} \\ & =\frac{1}{2} \end{align}$ Substitute $y=-2$ in $x={{2}^{y}}$: $\begin{align} & x={{2}^{-2}} \\ & =\frac{1}{{{2}^{2}}} \\ & =\frac{1}{4} \end{align}$ Tabulate the obtained values as shown below: $\begin{matrix} x & y \\ 1 & 0 \\ 2 & 1 \\ 4 & 2 \\ \frac{1}{2} & -1 \\ \frac{1}{4} & -2 \\ \end{matrix}$ Now, draw the graph of $y={{\log }_{2}}x$
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