Chapter 7.3, Problem 64HP

(a)

To determine

To Find: The logarithm expression of form $y={\log }_{b}x$

Answer to Problem 64HP

  $25={\log }_{2}33554432$

Explanation of Solution

Given: $y=25$

Equation:

  $\begin{array}{l}y={\log }_{b}x\\ b^y=x\end{array}$

Here

  $y=25$

  $\begin{array}{l}25={\log }_{b}x\\ i.e.\\ 25={\log }_{2}33554432\end{array}$

Hence,

  $25={\log }_{2}33554432$

(b)

To determine

To Find: The logarithm expression of form $y={\log }_{b}x$

Answer to Problem 64HP

  $-1={\log }_2\frac{1}{2}$

Explanation of Solution

Given: $y$ is negative

Equation:

  $y={\log }_{b}x$

Here

  $y$ is negative

  $\begin{array}{l}-1={\log }_{b}x\\ i.e.\\ -1={\log }_{2}x\\ -1={\log }_2\frac{1}{2}\end{array}$

Hence,

  $-1={\log }_2\frac{1}{2}$

(c)

To determine

To Find: The logarithm expression of form $y={\log }_{b}x$

Answer to Problem 64HP

  $0.5={\log }_{2}1.41$

Explanation of Solution

Given: $y$ is between $0and1$

Equation:

  $y={\log }_{b}x$

Here

  $y$ is between $0and1$

  $\begin{array}{l}0.5={\log }_{b}x\\ i.e.\\ 0.5={\log }_{2}x\\ 0.5={\log }_{2}1.41\end{array}$

Hence,

  $0.5={\log }_{2}1.41$

(d)

To determine

To Find: The logarithm expression of form $y={\log }_{b}x$

Answer to Problem 64HP

  $0={\log }_{10}1$

Explanation of Solution

Given: $x=1$

Equation:

  $y={\log }_{b}x$

Here

  $x=1$

  $\begin{array}{l}y={\log }_{b}1\\ i.e.\\ y={\log }_{10}1\\ 0={\log }_{10}1\end{array}$

Hence,

  $0={\log }_{10}1$

(e)

To determine

To Find: The logarithm expression of form $y={\log }_{b}x$

Answer to Problem 64HP

Does not exist

Explanation of Solution

Given: $x=0$

Equation:

  $y={\log }_{b}x$

Here

  $x=0$

  $\begin{array}{l}y={\log }_{b}0\\ i.e.\\ a^b\ne 0\end{array}$

Hence,

This is not exists.