12.6: Exponential and Logarithmic Functions- Answers to the Homework Exercises

Last updated
Save as PDF

Page ID: 45122

$ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $ $ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} $$\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$ $\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$

Inverse Functions

no; $[-2,0]$ or $[0,2]$

$g^{-1}(x)=\dfrac{4-2x}{x}$

$f^{-1}(x)=-5x+10$

$f^{-1}(x)=\sqrt[3]{x}+3$

$f^{-1}(x)=\dfrac{-x-1}{x-1}$

$g^{-1}(x)=\dfrac{-x+1}{5}$

$h^{-1}(x)=\dfrac{(-2x+4)^3}{4}$

$f^{-1}(x)=\dfrac{2x+7}{x+3}$

$g^{-1}(x)=(x-2)^3-1$

$g^{-1}(x)=3x-9$

$f^{-1}(x)=\dfrac{-4x+12}{3}$

$f^{-1}(x)=\dfrac{-3x-3}{x+2}$

$g^{-1}(x)=-3x+2$

$f^{-1}(x)=\sqrt[5]{\dfrac{-x+3}{2}}$

$f^{-1}(x)=\dfrac{-1-x}{x}$

$g^{-1}(x)=\dfrac{-3x+1}{2}$

Exponential Functions

$clipboard_ea0bc9dd7eed5d6d992ec4f3dade0168f.png$
Figure 12.6.1

$clipboard_eb5010c572078bb5505dbf9ad12e43c27.png$
Figure 12.6.2

$clipboard_eb2b6e1703bd6b9cc45a861e599e83599.png$
Figure 12.6.3

$clipboard_ea10d64881fb4cac3ffcd6db266bcb080.png$
Figure 12.6.4

$0$

$-\dfrac{3}{4}$

$-\dfrac{2}{3}$

$-2$

No Solution

No Solution

No Solution

$0$

$\dfrac{1}{3}$

$\dfrac{3}{8}$

$-1$

$-\dfrac{5}{4}$

$0$

$-\dfrac{5}{6}$

$-\dfrac{4}{3}$

$0$

$\dfrac{1}{4}$

No Solution

$\dfrac{2}{3}$

$-1$

Logarithmic Functions

$9^2=81$

$13^2=169$

$16^2=256$

$\log_8 1=0$

$\log_{64}2=\dfrac{1}{6}$

$\log_{144}12=\dfrac{1}{2}$

$\dfrac{1}{3}$

$2$

$6$

$0$

$\dfrac{1}{2}$

$\left(-\dfrac{10}{7},\infty\right)$

$\left(-\infty, \dfrac{7}{8}\right)$

$clipboard_e457a3bcfbf277cd2601aa6db51ca25f6.png$
Figure 12.6.5

$clipboard_eafb08a5f34896db57ae3fa02dc04bcb3.png$
Figure 12.6.6

$clipboard_e473ce75a7a47795dc8531a6ffb9a0732.png$
Figure 12.6.7

$5$

$121$

$-\dfrac{125}{3}$

$-\dfrac{1}{2}$

$\dfrac{2}{5}$

$1,000$

$\dfrac{45}{11}$

$-\dfrac{2401}{3}$

$\dfrac{283}{243}$

Logarithm Properties

$\log_a\left(\dfrac{mk^{6}}{n}\right)$
$\log_8 6x$
$\log_8 (6x^3-12)$
$\log_a \left(\dfrac{a^2(2x+1)^3}{(2x-1)^2}\right)$
$3-\dfrac{1}{2}\log_4 (x-1)$
$2\log_2 x-6\log_2 y$
$\log_b x+3\log_b z$
$\log_b x+5\log_b y-7\log_b z$
$2.8540$
$-3.2694$
$1.3778$
$1$
$0.394$
$\sqrt{5}$
$0$

Solve Exponential and Logarithmic Functions

$\dfrac{377}{124}$
$10$
$6$
$8$
$9$
No Solution
$\dfrac{11}{5}$
$-7+\log_3 7$; $-5.2288$
$\dfrac{1}{8}\log_2 3.6$; $0.2310$
$\log_2 \dfrac{11}{10}$; $0.1375$
$\dfrac{1}{9}\log_5 39.2$; $0.2533$
$24.75$ years
year 2034
$105$ days
$10.5$ minutes