Question 1

Solve the equation.
-$3(10-2 x)=81$

Accepted Answer

A)  $\{5\}$ 
B)  $\{27\}$ 
C)  $\{-3\}$ 
D)  $\{3\}$ 
A)  $\{5\}$ 
B)  $\{27\}$ 
C)  $\{-3\}$ 
D)  $\{3\}$

Question 2

Using the exponential key of a calculator to find an approximation to the nearest thousandth.
-$17^{2.2}$

Accepted Answer

A)  $662,499.529$ 
B)  509.316 
C)  289 
D)  37.4 
A)  $662,499.529$ 
B)  509.316 
C)  289 
D)  37.4

Question 3

How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the function $\mathrm{A}(\mathrm{t})=250 \mathrm{e}^{-0.235 \mathrm{t}}$, where $\mathrm{t}$ is the time in years? Round your answer to the nearest hundredth year.

Accepted Answer

A)  $2.95 \mathrm{yr}$ 
B)  $23.50 \mathrm{yr}$ 
C)  $58.75 \mathrm{yr}$ 
D)  $26.45 \mathrm{yr}$ 
A)  $2.95 \mathrm{yr}$ 
B)  $23.50 \mathrm{yr}$ 
C)  $58.75 \mathrm{yr}$ 
D)  $26.45 \mathrm{yr}$

Question 4

The number of dislocated electric impulses per cubic inch in a transformer increases when lightning strikes by $\mathrm{D}=6600(2)^{\mathrm{x}}$, where $\mathrm{x}$ is the time in milliseconds of the lightning strike. Find the number of dislocated impulses at $\mathrm{x}=0$ and $\mathrm{x}=5$.

Accepted Answer

A)  13,$200 ; 211,200$ 
B)  $6600 ; 66,000$ 
C)  $6600 ; 211,200$ 
D)  $6600 ; 26,400$ 
A)  13,$200 ; 211,200$ 
B)  $6600 ; 66,000$ 
C)  $6600 ; 211,200$ 
D)  $6600 ; 26,400$

Question 5

Graph the function.
-$f(x)= 3^{x}$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 6

The loudness of a sound can be approximated by the formula $d=10 \log _{10} \frac{\mathrm{I}}{\mathrm{I}_{\mathrm{O}}}$, where $\mathrm{d}$ is the number of decibels. The higher the value of $d$, the louder the sound. Find the number of decibels when $\mathrm{I}=1000$ and $\mathrm{I}_{\mathrm{O}}=1$.

Accepted Answer

A)  13 decibels 
B)  30 decibels 
C)  3 decibels 
D)  1000 decibels 
A)  13 decibels 
B)  30 decibels 
C)  3 decibels 
D)  1000 decibels

Question 7

Suppose that the salinity $S$ of ocean water at a given depth $d$ is modeled by the equation $S(d)=30.8+1.5 \log (d+1)$, where $S$ is measured in grams salt per kilogram water and $d$ is measured in meters. What is the salinity when the depth is $557 \mathrm{~m}$ ? Round your answer to the nearest hundredth.

Accepted Answer

A)  $-26.68 \mathrm{~g}$ salt $/ \mathrm{kg}$ water 
B)  $34.92 \mathrm{~g}$ salt $/ \mathrm{kg}$ water 
C)  $83.10 \mathrm{~g}$ salt $/ \mathrm{kg}$ water 
D)  $86.10 \mathrm{~g}$ salt $/ \mathrm{kg}$ water 
A)  $-26.68 \mathrm{~g}$ salt $/ \mathrm{kg}$ water 
B)  $34.92 \mathrm{~g}$ salt $/ \mathrm{kg}$ water 
C)  $83.10 \mathrm{~g}$ salt $/ \mathrm{kg}$ water 
D)  $86.10 \mathrm{~g}$ salt $/ \mathrm{kg}$ water

Question 8

Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers.
-$\log _{15} \frac{7}{8}$

Accepted Answer

A)  $\log _{15} 7 \div \log _{15} 8$ 
B)  $\log _{15} 8-\log _{15} 7$ 
C)  $\log _{15} 7+\log _{15} 7$ 
D)  $\log _{15} 7-\log _{15} 8$ 
A)  $\log _{15} 7 \div \log _{15} 8$ 
B)  $\log _{15} 8-\log _{15} 7$ 
C)  $\log _{15} 7+\log _{15} 7$ 
D)  $\log _{15} 7-\log _{15} 8$

Question 9

Write in logarithmic form.
-$81^{-3 / 2}=\frac{1}{729}$

Accepted Answer

A)  $\log _{81}\left(\frac{3}{2}\right)=-\frac{1}{729}$ 
B)  $\log _{81}\left(\frac{1}{729}\right)=-\frac{3}{2}$ 
C)  $\log _{729} 81=-\frac{3}{2}$ 
D)  $\log _{3 / 2} 729=81$ 
A)  $\log _{81}\left(\frac{3}{2}\right)=-\frac{1}{729}$ 
B)  $\log _{81}\left(\frac{1}{729}\right)=-\frac{3}{2}$ 
C)  $\log _{729} 81=-\frac{3}{2}$ 
D)  $\log _{3 / 2} 729=81$

Question 10

Determine whether or not the function is one-to-one.
-$\{(19,-5),(14,1),(1,10)\}$

Accepted Answer

A) True 
 B)False

Question 11

Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers.
-$\log _{9} \frac{\sqrt[4]{19}}{s^{2} r}$

Accepted Answer

A)  $\log _{9} 19-\log _{9} s-\log _{9} r$ 
B)  $\frac{1}{4} \log _{9} 19-2 \log _{9} s-\log _{9} r$ 
C)  $4 \log _{9} 19-2 \log _{9} \mathrm{~s}-\log _{9} 4$ 
D)  $\frac{1}{4} \log _{9} 19-2 \log _{9} s-2 \log _{9} r$ 
A)  $\log _{9} 19-\log _{9} s-\log _{9} r$ 
B)  $\frac{1}{4} \log _{9} 19-2 \log _{9} s-\log _{9} r$ 
C)  $4 \log _{9} 19-2 \log _{9} \mathrm{~s}-\log _{9} 4$ 
D)  $\frac{1}{4} \log _{9} 19-2 \log _{9} s-2 \log _{9} r$

Question 12

Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1 .
-$\left(\log _{\mathrm{x}} \mathrm{x}-\log _{\mathrm{x}} \mathrm{y}\right)+3 \log _{\mathrm{x}} \mathrm{z}$

Accepted Answer

A)  $\log _{x} \frac{x z^{3}}{y}$ 
B)  $\log _{x} x z^{3} y$ 
C)  $\log _{x} \frac{3 x z}{y}$ 
D)  $\log _{x} \frac{x}{z^{3} y}$ 
A)  $\log _{x} \frac{x z^{3}}{y}$ 
B)  $\log _{x} x z^{3} y$ 
C)  $\log _{x} \frac{3 x z}{y}$ 
D)  $\log _{x} \frac{x}{z^{3} y}$

Question 13

The sales of a mature product (one which has passed its peak) are given by the function $S(t)=S_{0} e^{-a t}$, where $t$ is time in years. Find the sales after 25 years if $a=0.15$ and $S_{0}=16,600$.

Accepted Answer

A)  195 
B)  14,288 
C)  390 
D)  336 
A)  195 
B)  14,288 
C)  390 
D)  336

Question 14

Write in exponential form.
-$\log _{\sqrt{3}} \sqrt{3^{6}}=x$

Accepted Answer

A)  $\{\sqrt{6}\}$ 
B) $ \{18\}$ 
C) $ \{6\}$ 
D)  $\{9\}$ 
A)  $\{\sqrt{6}\}$ 
B) $ \{18\}$ 
C) $ \{6\}$ 
D)  $\{9\}$

Question 15

Graph the function.
-$f(x)=4-x$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 16

Solve the problem. Round your answer to the nearest tenth, when appropriate. Use the formula $\mathrm{pH}=-\log \left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$, as needed.
-Find the $\mathrm{pH}$ if $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=3.6 \times 10^{-14}$.

Accepted Answer

A)  13.7 
B)  -14.6 
C)  14.6 
D)  13.4 
A)  13.7 
B)  -14.6 
C)  14.6 
D)  13.4

Question 17

Write in exponential form.
-$\log _{3}\left(3^{7}\right)=x$

Accepted Answer

A)  $\left\{7^{3}\right\}$ 
B)  $\left\{3^{7}\right\}$ 
C) $ \{3\}$ 
D)  $\{7\}$ 
A)  $\left\{7^{3}\right\}$ 
B)  $\left\{3^{7}\right\}$ 
C) $ \{3\}$ 
D)  $\{7\}$

Question 18

$\$ 6500$ is invested at $10 \%$ compounded quarterly. In how many years will the account have grown to $\$ 11,500$ ? Round your answer to the nearest tenth of a year.

Accepted Answer

A)  1.1 years 
B)  5.8 years 
C)  10.6 years 
D)  6.0 years 
A)  1.1 years 
B)  5.8 years 
C)  10.6 years 
D)  6.0 years

Question 19

Write in exponential form.
-$\log _{5} x=-2$

Accepted Answer

A)  $\{-10\}$ 
B)  $\left\{\frac{1}{32}\right\}$ 
C)  $\left\{\frac{1}{25}\right\}$ 
D)  $\{3\}$ 
A)  $\{-10\}$ 
B)  $\left\{\frac{1}{32}\right\}$ 
C)  $\left\{\frac{1}{25}\right\}$ 
D)  $\{3\}$

Question 20

What are the domain and range for the equation $y=2^{x}$ ?

Accepted Answer

A)  Domain: $(\infty, \infty)$; range: $(0, \infty)$ 
B)  Domain: $(\infty, \infty)$; range: $(\infty, \infty)$ 
C)  Domain: $(0, \infty)$; range: $(\infty, \infty)$ 
D)  $(\infty, \infty)$; range: $[0, \infty)$ 
A)  Domain: $(\infty, \infty)$; range: $(0, \infty)$ 
B)  Domain: $(\infty, \infty)$; range: $(\infty, \infty)$ 
C)  Domain: $(0, \infty)$; range: $(\infty, \infty)$ 
D)  $(\infty, \infty)$; range: $[0, \infty)$

Solve the equation. - $3(10-2 x)=81$

Using the exponential key of a calculator to find an approximation to the nearest thousandth. - $17^{2.2}$

How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the function $\mathrm{A}(\mathrm{t})=250 \mathrm{e}^{-0.235 \mathrm{t}}$ , where $\mathrm{t}$ is the time in years? Round your answer to the nearest hundredth year.

The number of dislocated electric impulses per cubic inch in a transformer increases when lightning strikes by $\mathrm{D}=6600(2)^{\mathrm{x}}$ , where $\mathrm{x}$ is the time in milliseconds of the lightning strike. Find the number of dislocated impulses at $\mathrm{x}=0$ and $\mathrm{x}=5$ .

Graph the function. - $f(x)= 3^{x}$ $Graph the function. - f(x)= 3^{x}$

Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers. - $\log _{15} \frac{7}{8}$

Write in logarithmic form. - $81^{-3 / 2}=\frac{1}{729}$

Determine whether or not the function is one-to-one. - $\{(19,-5),(14,1),(1,10)\}$

Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers. - $\log _{9} \frac{\sqrt[4]{19}}{s^{2} r}$

Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1 . - $\left(\log _{\mathrm{x}} \mathrm{x}-\log _{\mathrm{x}} \mathrm{y}\right)+3 \log _{\mathrm{x}} \mathrm{z}$

The sales of a mature product (one which has passed its peak) are given by the function $S(t)=S_{0} e^{-a t}$ , where $t$ is time in years. Find the sales after 25 years if $a=0.15$ and $S_{0}=16,600$ .

Write in exponential form. - $\log _{\sqrt{3}} \sqrt{3^{6}}=x$

Graph the function. - $f(x)=4-x$

Solve the problem. Round your answer to the nearest tenth, when appropriate. Use the formula $\mathrm{pH}=-\log \left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ , as needed. -Find the $\mathrm{pH}$ if $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=3.6 \times 10^{-14}$ .

Write in exponential form. - $\log _{3}\left(3^{7}\right)=x$

$\$ 6500$ is invested at $10 \%$ compounded quarterly. In how many years will the account have grown to $\$ 11,500$ ? Round your answer to the nearest tenth of a year.

Write in exponential form. - $\log _{5} x=-2$

What are the domain and range for the equation $y=2^{x}$ ?

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 10: Inverse, Exponential, and Logarithmic Functions

Solve the equation. - 3(10−2x)=813(10-2 x)=813(10−2x)=81

Using the exponential key of a calculator to find an approximation to the nearest thousandth. - 172.217^{2.2}172.2

Graph the function. - f(x)=3xf(x)= 3^{x}f(x)=3x

Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers. - log⁡1578\log _{15} \frac{7}{8}log15​87​

Write in logarithmic form. - 81−3/2=172981^{-3 / 2}=\frac{1}{729}81−3/2=7291​

Determine whether or not the function is one-to-one. - {(19,−5),(14,1),(1,10)}\{(19,-5),(14,1),(1,10)\}{(19,−5),(14,1),(1,10)}

Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers. - log⁡9194s2r\log _{9} \frac{\sqrt[4]{19}}{s^{2} r}log9​s2r419​​

The sales of a mature product (one which has passed its peak) are given by the function S(t)=S0e−atS(t)=S_{0} e^{-a t}S(t)=S0​e−at , where ttt is time in years. Find the sales after 25 years if a=0.15a=0.15a=0.15 and S0=16,600S_{0}=16,600S0​=16,600 .

Write in exponential form. - log⁡336=x\log _{\sqrt{3}} \sqrt{3^{6}}=xlog3​​36​=x

Graph the function. - f(x)=4−xf(x)=4-xf(x)=4−x

Write in exponential form. - log⁡3(37)=x\log _{3}\left(3^{7}\right)=xlog3​(37)=x

$6500\$ 6500$6500 is invested at 10%10 \%10% compounded quarterly. In how many years will the account have grown to $11,500\$ 11,500$11,500 ? Round your answer to the nearest tenth of a year.

Write in exponential form. - log⁡5x=−2\log _{5} x=-2log5​x=−2

What are the domain and range for the equation y=2xy=2^{x}y=2x ?

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Solve the equation. - $3(10-2 x)=81$

Using the exponential key of a calculator to find an approximation to the nearest thousandth. - $17^{2.2}$

Graph the function. - $f(x)= 3^{x}$ $Graph the function. - f(x)= 3^{x}$

Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers. - $\log _{15} \frac{7}{8}$

Write in logarithmic form. - $81^{-3 / 2}=\frac{1}{729}$

Determine whether or not the function is one-to-one. - $\{(19,-5),(14,1),(1,10)\}$

Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers. - $\log _{9} \frac{\sqrt[4]{19}}{s^{2} r}$

The sales of a mature product (one which has passed its peak) are given by the function $S(t)=S_{0} e^{-a t}$ , where $t$ is time in years. Find the sales after 25 years if $a=0.15$ and $S_{0}=16,600$ .

Write in exponential form. - $\log _{\sqrt{3}} \sqrt{3^{6}}=x$

Graph the function. - $f(x)=4-x$

Write in exponential form. - $\log _{3}\left(3^{7}\right)=x$

$\$ 6500$ is invested at $10 \%$ compounded quarterly. In how many years will the account have grown to $\$ 11,500$ ? Round your answer to the nearest tenth of a year.

Write in exponential form. - $\log _{5} x=-2$

What are the domain and range for the equation $y=2^{x}$ ?