Chapter 3, Problem 8CT

a .

To determine

To evaluate: ${\log }_7{7}^{-0.89}$

Answer to Problem 8CT

  ${\log }_7{7}^{-0.89}=-0.89$

Explanation of Solution

Concept used:

1. Power property of logarithm states that for a positive real numbers a such that $a\ne 1$ :

  ${\log }_a{u}^n=n{\log }_{a}u$

2. ${\log }_{a}a=1$

Using the Power property of logarithm, the given expression can be written as:

  ${\log }_7{7}^{-0.89}=-0.89{\log }_{7}7$

Using the property ${\log }_{a}a=1$ ,

  $\begin{array}{c}{\log }_7{7}^{-0.89}=-0.89{\log }_{7}7\\ =-0.89\left(1\right)\\ =-0.89\end{array}$

b.

To determine

To evaluate: $4.6\ln e^2$

Answer to Problem 8CT

  $4.6\ln e^2=9.2$

Explanation of Solution

Concept used:

1. Power property of logarithm states that for natural logarithm:

  $\ln a^b=b\ln a$

2. $\ln e=1$

Using the Power property of logarithm, the given expression can be written as:

  $\begin{array}{c}4.6\ln e^2=4.6\times 2\ln e\\ =9.2\ln e\end{array}$

Using the property $\ln e=1$ ,

  $\begin{array}{c}4.6\ln e^2=9.2\ln e\\ =9.2\left(1\right)\\ =9.2\end{array}$ .