Question 1

Solve the logarithmic equation. Check the solution.  log⁡(x2+7x) =log⁡(x2+56) \log \left( x ^ { 2 } + 7 x \right)  = \log \left( x ^ { 2 } + 56 \right) log(x2+7x) =log(x2+56)

Accepted Answer

A)  x = 9
B)  x = 8
C)  x = 11
D)  x = 10

Question 2

Graph  y=log⁡14xy = \log _ { \frac { 1 } { 4 } } xy=log41​​x  by graphing  (14) y=x\left( \frac { 1 } { 4 } \right)  ^ { y } = x(41​) y=x  .

Accepted Answer

A)   
B)   
C)

Question 3

Find the value of  xxx  .  log⁡381=x\log _ { 3 } 81 = xlog3​81=x

Accepted Answer

A)  3
B)  5
C)  6
D)  2
E)  4

Question 4

Evaluate the following.  log⁡b1\log _ { b } 1logb​1

Accepted Answer

A)  0
B)    bbb 
C)  1
D)    1b\frac { 1 } { b }b1​ 
E)  none of these

Question 5

Solve the equation log 3 (2 x - 1) - log 3 ( x - 2) = 1.

Accepted Answer

A)  x = 4
B)  x = 5
C)  x = 2
D)  x = 7
E)  x = 6

Question 6

Solve the equation log 6  x = 2.

Accepted Answer

A)  x = 64
B)  x = 42
C)  x = 2
D)  x = 6
E)  x = 36

Question 7

Graph  y=log⁡6xy = \log _ { 6 } xy=log6​x  by reflecting the graph of  g(x) =6xg ( x )  = 6 ^ { x }g(x) =6x  across the line y = x .

Accepted Answer

A)   
B)   
C)

Question 8

Solve the logarithmic equation. Check the solution.  log⁡(8x+5) −log⁡(7x+8) =0\log ( 8 x + 5 )  - \log ( 7 x + 8 )  = 0log(8x+5) −log(7x+8) =0

Accepted Answer

A)  x = 1
B)  x = 0
C)  x = 3
D)  x = 4

Question 9

Use your calculator to find x when given ln x . Express answer to four decimal places.  ln⁡x=2.5138\ln x = 2.5138lnx=2.5138

Accepted Answer

A)  12.4018
B)  12.3418
C)  12.3818
D)  12.3518
E)  12.3718

Question 10

Use a calculator and the change-of-base formula to find the logarithm to four decimal places.  log⁡3π\log _ { 3 } \pilog3​π

Accepted Answer

A)  0.6189
B)  1.0420
C)  1.8074
D)  1.0342
E)  0.9415

Question 11

Assume that  xxx  ,  yyy  ,  zzz  , and   a 	ext { a } a    (b≠1) ( b 
eq 1 ) (b=1)   are positive numbers.Use the properties of logarithms to write the expression in terms of the logarithms of x , y , and z .  log⁡bxyz\log _ { b } \frac { x } { y z }logb​yzx​

Accepted Answer

A)  log b  x log b  y log b  z
B)  log b  x + log b  y + log b  z
C)  - log b  x - log b  y - log b  z
D)  log b  x - log b  y - log b  z

Question 12

The half-life of radium is approximately 1,600 years. If the present amount of radium in a certain location is 900 grams, how much will remain after 400 years? Express your answer to the nearest gram.

Accepted Answer

A)  Q = 734 gram
B)  Q = 768 gram
C)  Q = 757 gram
D)  Q = 752 gram
E)  Q = 744 gram

Question 13

Graph the exponential function.  f(x) =e−xf ( x )  = e ^ { - x }f(x) =e−x

Accepted Answer

A)   
B)   
C)   
D)

Question 14

Graph the exponential function.  f(x) =(13) xf ( x )  = \left( \frac { 1 } { 3 } \right)  ^ { x }f(x) =(31​) x

Accepted Answer

A)   
B)   
C)   
D)

Question 15

Use a calculator and the change-of-base formula to find the logarithm to four decimal places.  log⁡133\log _ { \frac { 1 } { 3 } } 3log31​​3

Accepted Answer

A)  0.5769
B)  - 1.0000
C)  1.1005
D)  - 1.0078
E)  1.7654

Question 16

Solve the exponential equation and express approximate solutions to the nearest hundredth. e x - 4 = 38

Accepted Answer

A)  x = 7.11
B)  x = 4.00
C)  x = 8.17
D)  x = 7.64
E)  x = 7.52

Question 17

Assume that  xxx  ,  yyy  ,  ZZZ  , and  b(b≠1) b ( b 
eq 1 ) b(b=1)   are positive numbers Use the properties of logarithms to write the expression in terms of the logarithms of  xxx  ,  yyy  , and  ZZZ  .  log⁡bxy5z6\log _ { b } x y ^ { 5 } z ^ { 6 }logb​xy5z6

Accepted Answer

A)    log⁡bx+log⁡by5+log⁡bz6\log _ { b } x + \frac { \log _ { b } y } { 5 } + \frac { \log _ { b } z } { 6 }logb​x+5logb​y​+6logb​z​ 
B)    log⁡bx+(log⁡by) 5+(log⁡bz) 6\log _ { b } x + \left( \log _ { b } y \right)  ^ { 5 } + \left( \log _ { b } z \right)  ^ { 6 }logb​x+(logb​y) 5+(logb​z) 6 
C)    log⁡bx+5log⁡by+6log⁡bz\log _ { b } x + 5 \log _ { b } y + 6 \log _ { b } zlogb​x+5logb​y+6logb​z 
D)    −log⁡bx−5log⁡by−6log⁡bz- \log _ { b } x - 5 \log _ { b } y - 6 \log _ { b } z−logb​x−5logb​y−6logb​z 
E)    log⁡bx−log⁡by5−log⁡bz6\log _ { b } x - \frac { \log _ { b } y } { 5 } - \frac { \log _ { b } z } { 6 }logb​x−5logb​y​−6logb​z​

Exam 11: Exponential and Logarithmic Functions

Solve the logarithmic equation. Check the solution. $\log ( 8 x + 5 ) - \log ( 7 x + 8 ) = 0$

Correct Answer
verified

Solve the exponential equation and express approximate solutions to the nearest hundredth. e^{x - 4} = 38

Correct Answer
verified

Solve the logarithmic equation. Check the solution. $\log \left( x ^ { 2 } + 7 x \right) = \log \left( x ^ { 2 } + 56 \right)$

Correct Answer
verified

Use a calculator and the change-of-base formula to find the logarithm to four decimal places. $\log _ { \frac { 1 } { 3 } } 3$

Correct Answer
verified

Graph $y = \log _ { 6 } x$ by reflecting the graph of $g ( x ) = 6 ^ { x }$ across the line y = x .

Correct Answer
verified

Solve the equation log₆ x = 2.

Correct Answer
verified

Assume that $x$ , $y$ , $Z$ , and $b ( b \neq 1 )$ are positive numbers Use the properties of logarithms to write the expression in terms of the logarithms of $x$ , $y$ , and $Z$ . $\log _ { b } x y ^ { 5 } z ^ { 6 }$

Correct Answer
verified

Evaluate the following. $\log _ { b } 1$

Correct Answer
verified

Use a calculator and the change-of-base formula to find the logarithm to four decimal places. $\log _ { 3 } \pi$

Correct Answer
verified

The half-life of radium is approximately 1,600 years. If the present amount of radium in a certain location is 900 grams, how much will remain after 400 years? Express your answer to the nearest gram.

Correct Answer
verified

Solve the equation log₃ (2 x - 1) - log₃ ( x - 2) = 1.

Correct Answer
verified

Graph the exponential function. $f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$

Correct Answer
verified

Find the value of $x$ . $\log _ { 3 } 81 = x$

Correct Answer
verified

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

Correct Answer
verified

Assume that $x$ , $y$ , $z$ , and $\text { a }$ $( b \neq 1 )$ are positive numbers.Use the properties of logarithms to write the expression in terms of the logarithms of x , y , and z . $\log _ { b } \frac { x } { y z }$

Correct Answer
verified

Graph $y = \log _ { \frac { 1 } { 4 } } x$ by graphing $\left( \frac { 1 } { 4 } \right) ^ { y } = x$ .

Correct Answer
verified

Use your calculator to find x when given ln x . Express answer to four decimal places. $\ln x = 2.5138$

Correct Answer
verified

Exam 11: Exponential and Logarithmic Functions

Solve the logarithmic equation. Check the solution. log⁡(8x+5) −log⁡(7x+8) =0\log ( 8 x + 5 ) - \log ( 7 x + 8 ) = 0log(8x+5) −log(7x+8) =0

Correct AnswerverifiedShow Answer

Solve the exponential equation and express approximate solutions to the nearest hundredth. e x - 4 = 38

Correct AnswerverifiedShow Answer

Solve the logarithmic equation. Check the solution. log⁡(x2+7x) =log⁡(x2+56) \log \left( x ^ { 2 } + 7 x \right) = \log \left( x ^ { 2 } + 56 \right) log(x2+7x) =log(x2+56)

Correct AnswerverifiedShow Answer

Use a calculator and the change-of-base formula to find the logarithm to four decimal places. log⁡133\log _ { \frac { 1 } { 3 } } 3log31​​3

Correct AnswerverifiedShow Answer

Graph y=log⁡6xy = \log _ { 6 } xy=log6​x by reflecting the graph of g(x) =6xg ( x ) = 6 ^ { x }g(x) =6x across the line y = x .

Correct AnswerverifiedShow Answer

Solve the equation log 6 x = 2.

Correct AnswerverifiedShow Answer

Assume that xxx , yyy , ZZZ , and b(b≠1) b ( b \neq 1 ) b(b=1) are positive numbers Use the properties of logarithms to write the expression in terms of the logarithms of xxx , yyy , and ZZZ . log⁡bxy5z6\log _ { b } x y ^ { 5 } z ^ { 6 }logb​xy5z6

Correct AnswerverifiedShow Answer

Evaluate the following. log⁡b1\log _ { b } 1logb​1

Correct AnswerverifiedShow Answer

Use a calculator and the change-of-base formula to find the logarithm to four decimal places. log⁡3π\log _ { 3 } \pilog3​π

Correct AnswerverifiedShow Answer

The half-life of radium is approximately 1,600 years. If the present amount of radium in a certain location is 900 grams, how much will remain after 400 years? Express your answer to the nearest gram.

Correct AnswerverifiedShow Answer

Solve the equation log 3 (2 x - 1) - log 3 ( x - 2) = 1.

Correct AnswerverifiedShow Answer

Graph the exponential function. f(x) =(13) xf ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }f(x) =(31​) x

Correct AnswerverifiedShow Answer

Find the value of xxx . log⁡381=x\log _ { 3 } 81 = xlog3​81=x

Correct AnswerverifiedShow Answer

Graph the exponential function. f(x) =e−xf ( x ) = e ^ { - x }f(x) =e−x

Correct AnswerverifiedShow Answer

Assume that xxx , yyy , zzz , and a \text { a } a (b≠1) ( b \neq 1 ) (b=1) are positive numbers.Use the properties of logarithms to write the expression in terms of the logarithms of x , y , and z . log⁡bxyz\log _ { b } \frac { x } { y z }logb​yzx​

Correct AnswerverifiedShow Answer

Graph y=log⁡14xy = \log _ { \frac { 1 } { 4 } } xy=log41​​x by graphing (14) y=x\left( \frac { 1 } { 4 } \right) ^ { y } = x(41​) y=x .

Correct AnswerverifiedShow Answer

Use your calculator to find x when given ln x . Express answer to four decimal places. ln⁡x=2.5138\ln x = 2.5138lnx=2.5138

Correct AnswerverifiedShow Answer

Solve the logarithmic equation. Check the solution. $\log ( 8 x + 5 ) - \log ( 7 x + 8 ) = 0$

Correct Answer
verified

Solve the exponential equation and express approximate solutions to the nearest hundredth. e^{x - 4} = 38

Correct Answer
verified

Solve the logarithmic equation. Check the solution. $\log \left( x ^ { 2 } + 7 x \right) = \log \left( x ^ { 2 } + 56 \right)$

Correct Answer
verified

Use a calculator and the change-of-base formula to find the logarithm to four decimal places. $\log _ { \frac { 1 } { 3 } } 3$

Correct Answer
verified

Graph $y = \log _ { 6 } x$ by reflecting the graph of $g ( x ) = 6 ^ { x }$ across the line y = x .

Correct Answer
verified

Solve the equation log₆ x = 2.

Correct Answer
verified

Assume that $x$ , $y$ , $Z$ , and $b ( b \neq 1 )$ are positive numbers Use the properties of logarithms to write the expression in terms of the logarithms of $x$ , $y$ , and $Z$ . $\log _ { b } x y ^ { 5 } z ^ { 6 }$

Correct Answer
verified

Evaluate the following. $\log _ { b } 1$

Correct Answer
verified

Use a calculator and the change-of-base formula to find the logarithm to four decimal places. $\log _ { 3 } \pi$

Correct Answer
verified

Correct Answer
verified

Solve the equation log₃ (2 x - 1) - log₃ ( x - 2) = 1.

Correct Answer
verified

Graph the exponential function. $f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$

Correct Answer
verified

Find the value of $x$ . $\log _ { 3 } 81 = x$

Correct Answer
verified

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

Correct Answer
verified

Assume that $x$ , $y$ , $z$ , and $\text { a }$ $( b \neq 1 )$ are positive numbers.Use the properties of logarithms to write the expression in terms of the logarithms of x , y , and z . $\log _ { b } \frac { x } { y z }$

Correct Answer
verified

Graph $y = \log _ { \frac { 1 } { 4 } } x$ by graphing $\left( \frac { 1 } { 4 } \right) ^ { y } = x$ .

Correct Answer
verified

Use your calculator to find x when given ln x . Express answer to four decimal places. $\ln x = 2.5138$

Correct Answer
verified