Basic Technical Mathematics, 11th Edition

CHAPTER 13 PRACTICE TEST

As a study aid, we have included complete solutions for each Practice Test problem at the end of this book.

In Problems 1–4, determine the value of x.

1. ${\log }_{9}x\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}{\displaystyle \frac{1}{2}}$

2. ${\log }_{3}x\hspace{0.17em}-\hspace{0.17em}{\log }_{3}2\hspace{0.17em}=\hspace{0.17em}2$

3. ${\log }_{x}64\hspace{0.17em}=\hspace{0.17em}3$

4. $3^{3x\hspace{0.17em}+\hspace{0.17em}1}\hspace{0.17em}=\hspace{0.17em}8$

5. Graph the function $y\hspace{0.17em}=\hspace{0.17em}2{\log }_{4}x\hspace{0.17em}.\hspace{0.17em}$

6. Graph the function $y\hspace{0.17em}=\hspace{0.17em}2(3^x)$ on semilog paper.

7. Express ${\log }_5\left({\displaystyle \frac{4a^3}{7}}\right)$ as a combination of a sum, difference, and multiple of logarithms, including ${\log }_{5}2.$

8. Solve for y in terms of $x\hspace{0.17em}: \hspace{0.17em}3{\log }_{7}x\hspace{0.17em}-\hspace{0.17em}{\log }_{7}y\hspace{0.17em}=\hspace{0.17em}2.$

9. An equation used for a certain electric circuit is $\ln i\hspace{0.17em}-\hspace{0.17em}\ln I\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}t\hspace{0.17em}/\hspace{0.17em}RC\hspace{0.17em}.\hspace{0.17em}$ Solve for i.

10. Evaluate: ${\displaystyle \frac{2\ln 0.9523}{\log 6066}}\hspace{0.17em}.\hspace{0.17em}$

11. Evaluate: ${\log }_{5}732.$

12. If $A_0$ dollars are invested at 8%, compounded continuously for t years, the value A of the investment is given by $A\hspace{0.17em}=\hspace{0.17em}{A}_0{e}^{0.08t}\hspace{0.17em}.\hspace{0.17em}$ Determine how ...