Question 1

Write in exponential form: $\log _ { a } x = y$

Accepted Answer

A)  $a ^ { y } = x$ 
B)  $y ^ { a } = x$ 
C)  $a ^ { x } = y$ 
D)  $x ^ { y } = a$ 
A)  $a ^ { y } = x$ 
B)  $y ^ { a } = x$ 
C)  $a ^ { x } = y$ 
D)  $x ^ { y } = a$

Question 2

Let $f ( x ) = 6 x - 5$ and $g ( x ) = x ^ { 2 } + x$ . Find the composition. $( f \circ g ) ( - 3 )$

Accepted Answer

The answer of Let \(f ( x ) = 6...

Question 3

Graph the inverse of the following one-to-one function.

Accepted Answer

The answer of Graph the inverse of the following one-to-one...

Question 4

Exponential functions have a constant base and a variable _________.

Accepted Answer

The answer of Exponential functions have a constant base and...

Question 5

Solve the equation. $2 \log ( y + 2 ) = \log ( y + 2 ) - \log 11$ If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Solve the equation. \(2 \log ( y...

Question 6

The inverse of anexponential function is called a(n) __________ function.

Accepted Answer

The answer of The inverse of anexponential function is called...

Question 7

$\log _ { 7 } \frac { x y } { 7 }$ is called the __________ logarithmic function. The base is __________.

Accepted Answer

The answer of \(\log _ { 7 } \frac {...

Question 8

An account now contains $10,186 and has been accumulating interest at 4% annual interest, compounded continuously, for 6 years. Find the initial deposit. Round answer to the nearest cent.

Accepted Answer

A)  $12,948.94 
B)  $9,786.60 
C)  $8,012.59 
D)  $8,050.14 
A)  $12,948.94 
B)  $9,786.60 
C)  $8,012.59 
D)  $8,050.14

Question 9

Use the properties of logarithms to write $5 \log x + 4 \log y$ as the logarithm of a single quantity. Assume x and y are positive numbers.

Accepted Answer

A)  $\log \left( \frac { x ^ { 5 } } { y ^ { 4 } } \right)$ 
B)  $\log \left( x ^ { 5 } y ^ { 4 } \right)$ 
C)  $\log \left( \frac { 5 x } { 4 y } \right)$ 
D)  $\frac { \log x ^ { 5 } } { \log y ^ { 4 } }$ 
A)  $\log \left( \frac { x ^ { 5 } } { y ^ { 4 } } \right)$ 
B)  $\log \left( x ^ { 5 } y ^ { 4 } \right)$ 
C)  $\log \left( \frac { 5 x } { 4 y } \right)$ 
D)  $\frac { \log x ^ { 5 } } { \log y ^ { 4 } }$

Question 10

The half-life of tritium is 12.4 years. How long will it take for 15% of a sample of tritium to decompose?
 Please round the answer to the nearest tenth.

Accepted Answer

The answer of The half-life of tritium is 12.4 years....

Question 11

The graph of $f ( x ) = \ln x$ has the __________-intercept $( 1,0 )$ . The __________-axis is an asymptote of the graph.

Accepted Answer

The answer of The graph of \(f ( x )...

Question 12

Which of the following statements is true for a one-to-one function.

Accepted Answer

A)  A vertical line intersects the graph in more than one point. 
B)  A horizontal line intersects the graph in more than one point. 
C)  A horizontal line intersects the graph in at most one point. 
D)  none of these 
A)  A vertical line intersects the graph in more than one point. 
B)  A horizontal line intersects the graph in more than one point. 
C)  A horizontal line intersects the graph in at most one point. 
D)  none of these

Question 13

An initial deposit of $5000 grows at an annual rate of 8.9% for 5 years. Compare the final balances resulting from annual compounding and continuous compounding. Please round the answers to the nearest cent. $__________ from annual compounding. $__________ from continuous compounding.

Accepted Answer

The answer of An initial deposit of $5000 grows at...

Question 14

A population growing continuously at an annual rate r will triple in a time t given by the formula $t = \frac { \ln 3 } { r }$ . How long will it take the population of a town to triple if it is growing at the rate of 13% per year?
 Please round the answer to one decimal place. __________ yr

Accepted Answer

The answer of A population growing continuously at an annual...

Question 15

Solve the equation. $\log ( 4 - 3 x ) - \log ( x + 32 ) = 0$ If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Solve the equation. \(\log ( 4 -...

Question 16

$f ( x ) = \ln x$ and $g ( x ) = e ^ { x }$ are __________ functions.

Accepted Answer

The answer of $f ( x ) = \ln x$...

Question 17

Let $f ( x ) = 4 x + 3$ and $g ( x ) = x ^ { 2 } - 1$. Find the composition. $( f \circ g ) ( x )$

Accepted Answer

The answer of Let \(f ( x ) = 4...

Question 18

Solve: $3 ^ { 3 x - 3 } = 729$

Accepted Answer

A)  {3} 
B)  {2} 
C)  $\left\{ \frac { 7 } { 2 } \right\}$ 
D)  $\left\{ \frac { 1 } { 2 } \right\}$ 
A)  {3} 
B)  {2} 
C)  $\left\{ \frac { 7 } { 2 } \right\}$ 
D)  $\left\{ \frac { 1 } { 2 } \right\}$

Question 19

Evaluate expression without using a calculator. $\ln \frac { 1 } { e ^ { 10 } }$

Accepted Answer

The answer of Evaluate expression without using a calculator. \(\ln...

Question 20

Solve the equation. Give your answer to four decimal places. ${ } ^ { 227 } \mathrm { Th }$

Accepted Answer

The answer of Solve the equation. Give your answer to...

Write in exponential form: $\log _ { a } x = y$

Let $f ( x ) = 6 x - 5$ and $g ( x ) = x ^ { 2 } + x$ . Find the composition. $( f \circ g ) ( - 3 )$

Graph the inverse of the following one-to-one function.

Exponential functions have a constant base and a variable _________.

Solve the equation. $2 \log ( y + 2 ) = \log ( y + 2 ) - \log 11$ If there is more than one solution, separate your answers with commas.

The inverse of anexponential function is called a(n) __________ function.

$\log _ { 7 } \frac { x y } { 7 }$ is called the logarithmic function. The base is .

An account now contains $10,186 and has been accumulating interest at 4% annual interest, compounded continuously, for 6 years. Find the initial deposit. Round answer to the nearest cent.

Use the properties of logarithms to write $5 \log x + 4 \log y$ as the logarithm of a single quantity. Assume x and y are positive numbers.

The half-life of tritium is 12.4 years. How long will it take for 15% of a sample of tritium to decompose? Please round the answer to the nearest tenth.

The graph of $f ( x ) = \ln x$ has the -intercept $( 1,0 )$ . The -axis is an asymptote of the graph.

Which of the following statements is true for a one-to-one function.

An initial deposit of $5000 grows at an annual rate of 8.9% for 5 years. Compare the final balances resulting from annual compounding and continuous compounding. Please round the answers to the nearest cent. $ from annual compounding. $ from continuous compounding.

A population growing continuously at an annual rate r will triple in a time t given by the formula $t = \frac { \ln 3 } { r }$ . How long will it take the population of a town to triple if it is growing at the rate of 13% per year? Please round the answer to one decimal place. __________ yr

Solve the equation. $\log ( 4 - 3 x ) - \log ( x + 32 ) = 0$ If there is more than one solution, separate your answers with commas.

$f ( x ) = \ln x$ and $g ( x ) = e ^ { x }$ are __________ functions.

Let $f ( x ) = 4 x + 3$ and $g ( x ) = x ^ { 2 } - 1$ . Find the composition. $( f \circ g ) ( x )$

Solve: $3 ^ { 3 x - 3 } = 729$

Evaluate expression without using a calculator. $\ln \frac { 1 } { e ^ { 10 } }$

Solve the equation. Give your answer to four decimal places. ${ } ^ { 227 } \mathrm { Th }$

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Exam 9: Exponential and Logarithmic Functions

Write in exponential form: log⁡ax=y\log _ { a } x = yloga​x=y

Let f(x)=6x−5f ( x ) = 6 x - 5f(x)=6x−5 and g(x)=x2+xg ( x ) = x ^ { 2 } + xg(x)=x2+x . Find the composition. (f∘g)(−3)( f \circ g ) ( - 3 )(f∘g)(−3)

Graph the inverse of the following one-to-one function.

Exponential functions have a constant base and a variable _________.

Solve the equation. 2log⁡(y+2)=log⁡(y+2)−log⁡112 \log ( y + 2 ) = \log ( y + 2 ) - \log 112log(y+2)=log(y+2)−log11 If there is more than one solution, separate your answers with commas.

The inverse of anexponential function is called a(n) __________ function.

log⁡7xy7\log _ { 7 } \frac { x y } { 7 }log7​7xy​ is called the __________ logarithmic function. The base is __________.

An account now contains $10,186 and has been accumulating interest at 4% annual interest, compounded continuously, for 6 years. Find the initial deposit. Round answer to the nearest cent.

Use the properties of logarithms to write 5log⁡x+4log⁡y5 \log x + 4 \log y5logx+4logy as the logarithm of a single quantity. Assume x and y are positive numbers.

The half-life of tritium is 12.4 years. How long will it take for 15% of a sample of tritium to decompose? Please round the answer to the nearest tenth.

The graph of f(x)=ln⁡xf ( x ) = \ln xf(x)=lnx has the __________-intercept (1,0)( 1,0 )(1,0) . The __________-axis is an asymptote of the graph.

Which of the following statements is true for a one-to-one function.

An initial deposit of $5000 grows at an annual rate of 8.9% for 5 years. Compare the final balances resulting from annual compounding and continuous compounding. Please round the answers to the nearest cent. $__________ from annual compounding. $__________ from continuous compounding.

Solve the equation. log⁡(4−3x)−log⁡(x+32)=0\log ( 4 - 3 x ) - \log ( x + 32 ) = 0log(4−3x)−log(x+32)=0 If there is more than one solution, separate your answers with commas.

f(x)=ln⁡xf ( x ) = \ln xf(x)=lnx and g(x)=exg ( x ) = e ^ { x }g(x)=ex are __________ functions.

Let f(x)=4x+3f ( x ) = 4 x + 3f(x)=4x+3 and g(x)=x2−1g ( x ) = x ^ { 2 } - 1g(x)=x2−1 . Find the composition. (f∘g)(x)( f \circ g ) ( x )(f∘g)(x)

Solve: 33x−3=7293 ^ { 3 x - 3 } = 72933x−3=729

Evaluate expression without using a calculator. ln⁡1e10\ln \frac { 1 } { e ^ { 10 } }lne101​

Solve the equation. Give your answer to four decimal places. 227Th{ } ^ { 227 } \mathrm { Th }227Th

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Write in exponential form: $\log _ { a } x = y$

Let $f ( x ) = 6 x - 5$ and $g ( x ) = x ^ { 2 } + x$ . Find the composition. $( f \circ g ) ( - 3 )$

Solve the equation. $2 \log ( y + 2 ) = \log ( y + 2 ) - \log 11$ If there is more than one solution, separate your answers with commas.

$\log _ { 7 } \frac { x y } { 7 }$ is called the logarithmic function. The base is .

Use the properties of logarithms to write $5 \log x + 4 \log y$ as the logarithm of a single quantity. Assume x and y are positive numbers.

The graph of $f ( x ) = \ln x$ has the -intercept $( 1,0 )$ . The -axis is an asymptote of the graph.

An initial deposit of $5000 grows at an annual rate of 8.9% for 5 years. Compare the final balances resulting from annual compounding and continuous compounding. Please round the answers to the nearest cent. $ from annual compounding. $ from continuous compounding.

Solve the equation. $\log ( 4 - 3 x ) - \log ( x + 32 ) = 0$ If there is more than one solution, separate your answers with commas.

$f ( x ) = \ln x$ and $g ( x ) = e ^ { x }$ are __________ functions.

Let $f ( x ) = 4 x + 3$ and $g ( x ) = x ^ { 2 } - 1$ . Find the composition. $( f \circ g ) ( x )$

Solve: $3 ^ { 3 x - 3 } = 729$

Evaluate expression without using a calculator. $\ln \frac { 1 } { e ^ { 10 } }$

Solve the equation. Give your answer to four decimal places. ${ } ^ { 227 } \mathrm { Th }$