Section 1
Exponential Functions
Write each expression in the form $2^{k x}$ or $3^{k x}$, for a suitable constant $k$. $4^{x},(\sqrt{3})^{x},\left(\frac{1}{9}\right)^{x}$
Write each expression in the form $2^{k x}$ or $3^{k x}$, for a suitable constant $k$. $27^{x},(\sqrt[3]{2})^{x},\left(\frac{1}{8}\right)^{x}$
Write each expression in the form $2^{k x}$ or $3^{k x}$, for a suitable constant $k$. $8^{2 x / 3}, 9^{3 x / 2}, 16^{-3 x / 4}$
Write each expression in the form $2^{k x}$ or $3^{k x}$, for a suitable constant $k$. $9^{-x / 2}, 8^{4 x / 3}, 27^{-2 x / 3}$
Write each expression in the form $2^{k x}$ or $3^{k x}$, for a suitable constant $k$. $\left(\frac{1}{4}\right)^{2 x},\left(\frac{1}{8}\right)^{-3 x},\left(\frac{1}{81}\right)^{x / 2}$
Write each expression in the form $2^{k x}$ or $3^{k x}$, for a suitable constant $k$. $\left(\frac{1}{9}\right)^{2 x},\left(\frac{1}{27}\right)^{x / 3},\left(\frac{1}{16}\right)^{-x / 2}$
Write each expression in the form $2^{k x}$ or $3^{k x}$, for a suitable constant $k$. $6^{x} \cdot 3^{-x}, \frac{15^{x}}{5^{x}}, \frac{12^{x}}{2^{2 x}}$
Write each expression in the form $2^{k x}$ or $3^{k x}$, for a suitable constant $k$. $7^{-x} \cdot 14^{x}, \frac{2^{x}}{6^{x}}, \frac{3^{2 x}}{18^{x}}$
Write each expression in the form $2^{k x}$ or $3^{k x}$, for a suitable constant $k$. $\frac{3^{4 x}}{3^{2 x}}, \frac{2^{5 x+1}}{2 \cdot 2^{-x}}, \frac{9^{-x}}{27^{-x / 3}}$
Write each expression in the form $2^{k x}$ or $3^{k x}$, for a suitable constant $k$. $\frac{2^{x}}{6^{x}}, \frac{3^{-5 x}}{3^{-2 x}}, \frac{16^{x}}{8^{-x}}$
Write each expression in the form $2^{k x}$ or $3^{k x}$, for a suitable constant $k$. $2^{3 x} \cdot 2^{-5 x / 2}, 3^{2 x}-\left(\frac{1}{3}\right)^{2 x / 3}$
Write each expression in the form $2^{k x}$ or $3^{k x}$, for a suitable constant $k$. $2^{5 x / 4} \cdot\left(\frac{1}{2}\right)^{x}, 3^{-2 x} \cdot 3^{5 x / 2}$
Write each expression in the form $2^{k x}$ or $3^{k x}$, for a suitable constant $k$. $\left(2^{-3 x} \cdot 2^{-2 x}\right)^{2 / 5},\left(9^{1 / 2}-9^{4}\right)^{x / 9}$
Write each expression in the form $2^{k x}$ or $3^{k x}$, for a suitable constant $k$. . $\left(3^{-x} \cdot 3^{x / 5}\right)^{5},\left(16^{1 / 4} \cdot 16^{-3 / 4}\right)^{3 a}$
Find a number $b$ such that the function $f(x)=3^{-2 x}$ can be written in the form $f(x)=b^{x}$.
Find $b$ so that $8^{-x / 3}=b^{x}$ for all $x$.
Solve the following equations for $x$ $5^{2 x}=5^{2}$
Solve the following equations for $x$ $10^{-x}=10^{2}$
Solve the following equations for $x$ $(2.5)^{2 x+1}=(2.5)^{5}$
Solve the following equations for $x$ $(3.2)^{x-3}=(3.2)^{5}$
Solve the following equations for $x$ $10^{1-z}=100$
Solve the following equations for $x$ $2^{4-x}=8$
Solve the following equations for $x$ $3(2.7)^{5 x}=8.1$
Solve the following equations for $x$ $4(2.7)^{2 x-1}=10.8$
Solve the following equations for $x$ . $\left(2^{x+1} \cdot 2^{-3}\right)^{2}=2$
Solve the following equations for $x$ $\left(3^{2 x} \cdot 3^{2}\right)^{4}=3$
Solve the following equations for $x$ $2^{3 x}=4 \cdot 2^{5 x}$
Solve the following equations for $x$ $3^{5 x} \cdot 3^{x}-3=0$
Solve the following equations for $x$ $(1+x) 2^{-x}-5 \cdot 2^{-r}=0$
Solve the following equations for $x$ $(2-3 x) 5^{x}+4 \cdot 5^{x}=0$
Solve the following equations for $x$ $2^{x}-\frac{8}{2^{2 x}}=0$
Solve the following equations for $x$ $2^{x}-\frac{1}{2^{x}}=0$
Solve the following equations for $x$ $2^{2 x}-6 \cdot 2^{x}+8=0$
Solve the following equations for $x$ $2^{2 x+2}-17 \cdot 2^{x}+4=0$
Solve the following equations for $x$ $3^{2 x}-12 \cdot 3^{x}+27=0$
Solve the following equations for $x$ $2^{2 x}-4 \cdot 2^{x}-32=0$
Find the missing factors.$2^{3+h}=2^{3}(\quad)$
Find the missing factors.$5^{2+h}=25(\quad)$
Find the missing factors.$2^{x+h}-2^{x}=2^{x}(\quad)$
Find the missing factors.$5^{x+h}+5^{x}=5^{x}(\quad)$
Find the missing factors. $3^{x / 2}+3^{-x / 2}=3^{-x / 2}(\quad)$
Find the missing factors.$5^{7 x / 2}-5^{x / 2}=\sqrt{5^{x}}(\quad)$
Graph the function $f(x)=2^{x}$ in the window $[-1,2]$ by $[-1,4]$, and estimate the slope of the graph at $x=0 .$
Graph the function $f(x)=3^{x}$ in the window $[-1,2]$ by $[-1,8]$, and estimate the slope of the graph at $x=0 .$
By trial and error, find a number of the form $b=2 . \square$ (just one decimal place) with the property that the slope of the graph of $y=b^{x}$ at $x=0$ is as close to 1 as possible.