# Chapter 4: Exponential and logarithmic functions

Q1.

Log *x* is the exponent to which the base 10 must be raised to get ____. So, we can complete the following table for log *x*.

Q1.

The function$f\left(x\right)={e}^{x}$is called the ______ exponential function. The number *e* is approximately equal to ______.

Q1.

The function$\mathit{f}\mathbf{\left(}\mathit{x}\mathbf{\right)}\mathbf{=}{\mathbf{5}}^{\mathbf{x}}$is an exponential function with base ____;

role="math" localid="1648559050478" $\mathit{f}\mathbf{(}\mathbf{-}\mathbf{2}\mathbf{)}\mathbf{=}\mathbf{\_}\mathbf{\_}\mathbf{\_}\mathbf{,}\mathbf{\text{\hspace{0.17em}\hspace{0.17em}}}\mathit{f}\mathbf{\left(}\mathbf{0}\mathbf{\right)}\mathbf{=}\mathbf{\_}\mathbf{\_}\mathbf{\_}\mathbf{,}\mathbf{\text{\hspace{0.17em}\hspace{0.17em}}}\mathit{f}\mathbf{\left(}\mathbf{2}\mathbf{\right)}\mathbf{=}\mathbf{\_}\mathbf{\_}\mathbf{\_}\mathbf{,}\mathbf{\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}}\mathit{f}\mathbf{\left(}\mathbf{6}\mathbf{\right)}\mathbf{=}\mathbf{\_}\mathbf{\_}\mathbf{\_}$

Q10.

Exponential Form Express the equation in exponential form.

(a) ${\mathrm{log}}_{5}\left(\frac{1}{5}\right)=-1$ (b)${\mathrm{log}}_{4}64=3$

Q10.

Graphing Exponential Functions Graph the function, not by plotting points, but by starting from the graph of $y={e}^{x}$in Figure 1. State the domain, range, and asymptote.

$y=1-{e}^{x}$

Q11.

Graphing Exponential Functions Graph the function, not by plotting points, but by starting from the graph of $y={e}^{x}$in Figure 1. State the domain, range, and asymptote.

$y={e}^{-x}-1$

Q11.

Exponential Form Express the equation in exponential form.

(a) ${\mathrm{log}}_{8}2=\frac{1}{3}$ (b)${\mathrm{log}}_{10}0.01=-2$

Q12.

Exponential Form Express the equation in exponential form.

(a) ${\mathrm{log}}_{5}\left(\frac{1}{125}\right)=-3$ (b)${\mathrm{log}}_{8}4=\frac{2}{3}$

Q12.

Graphing Exponential Functions Graph the function, not by plotting points, but by starting from the graph of $y={e}^{x}$in Figure 1. State the domain, range, and asymptote.

role="math" $f\left(x\right)=-{e}^{-x}$

Q13.

Exponential Form Express the equation in exponential form.

(a) ${\mathrm{log}}_{3}5=x$ (b)${\mathrm{log}}_{7}\left(3y\right)=2$