Question 1

Expand. Assume that all variables represent positive real numbers.
-$\log _ { d } \left( \frac { a ^ { 7 } b ^ { 5 } } { c ^ { 3 } d ^ { 6 } } \right)$

Accepted Answer

A)  $7 \log _ { d } a + 5 \log _ { d } b - 3 \log _ { d } c + 6$ 
B)  $7 \log _ { d } a + 5 \log _ { d } b - 3 \log _ { d } c - 6$ 
C)  $\log _ { \mathrm { d } } \mathrm { a } ^ { 7 } + \log _ { \mathrm { d } } \mathrm { b } ^ { 5 } + \log _ { \mathrm { d } } \mathrm { c } ^ { 3 } - \log _ { \mathrm { d } } \mathrm { b } ^ { 6 }$ 
D)  $a ^ { 7 } b ^ { 5 } - c ^ { 3 } d ^ { 6 }$ 
A)  $7 \log _ { d } a + 5 \log _ { d } b - 3 \log _ { d } c + 6$ 
B)  $7 \log _ { d } a + 5 \log _ { d } b - 3 \log _ { d } c - 6$ 
C)  $\log _ { \mathrm { d } } \mathrm { a } ^ { 7 } + \log _ { \mathrm { d } } \mathrm { b } ^ { 5 } + \log _ { \mathrm { d } } \mathrm { c } ^ { 3 } - \log _ { \mathrm { d } } \mathrm { b } ^ { 6 }$ 
D)  $a ^ { 7 } b ^ { 5 } - c ^ { 3 } d ^ { 6 }$ B

Question 2

Suppose for some base b > 0 (b ≠ 1) that logb 2 = A, logb 3 = B, logb 5 = C, and logb 7 = D. Express the given logarithms
in terms of A, B, C, or D.
-$\log _ { b } 6$

Accepted Answer

A)  $6 \mathrm {~A}$ 
B)  $- 6 \mathrm {~A}$ 
C)  $\mathrm { A } + \mathrm { C }$ 
D)  $\mathrm { A } + \mathrm { B }$ 
A)  $6 \mathrm {~A}$ 
B)  $- 6 \mathrm {~A}$ 
C)  $\mathrm { A } + \mathrm { C }$ 
D)  $\mathrm { A } + \mathrm { B }$ D

Question 3

Suppose for some base b > 0 (b ≠ 1) that logb 2 = A, logb 3 = B, logb 5 = C, and logb 7 = D. Express the given logarithms
in terms of A, B, C, or D.
-$\log _ { b } 125$

Accepted Answer

A)  $2 \mathrm { C }$ 
B)  $2 \mathrm { D }$ 
C)  $3 C$ 
D)  $3 \mathrm { D }$ 
A)  $2 \mathrm { C }$ 
B)  $2 \mathrm { D }$ 
C)  $3 C$ 
D)  $3 \mathrm { D }$ C

Question 4

Suppose for some base b > 0 (b ≠ 1) that logb 2 = A, logb 3 = B, logb 5 = C, and logb 7 = D. Express the given logarithms
in terms of A, B, C, or D.
-$\log _ { b } \left( \frac { 1 } { 125 } \right)$
A) $- 3 C$
B) $3 C$
C) $3 \mathrm { D }$
D) $- 3 \mathrm { D }$

Accepted Answer

The answer of Suppose for some base b > 0...

Question 5

Evaluate the given function.    
-$$f ( x ) = \log _ { 5 } x , f \left( \frac { 1 } { 25 } \right)$$

Accepted Answer

A)  $- 5$ 
B)  5 
C)  2 
D)  $- 2$ 
A)  $- 5$ 
B)  5 
C)  2 
D)  $- 2$

Question 6

Evaluate using the change-of-base formula. Round to four decimal places.
-$\log _ { 5 } 26.35$

Accepted Answer

A)  $0.4920$ 
B)  $5.2700$ 
C)  $2.0327$ 
D)  $1.4208$ 
A)  $0.4920$ 
B)  $5.2700$ 
C)  $2.0327$ 
D)  $1.4208$

Question 7

Solve.
-The number of acres in a landfill is given by the function B = 2800e-0.05t, where t is measured in years. How many acres will the landfill have after 2 years? (Round to the nearest acre.)

Accepted Answer

A)  2534 acres 
B)  2224 acres 
C)  2800 acres 
D)  6447 acres 
A)  2534 acres 
B)  2224 acres 
C)  2800 acres 
D)  6447 acres

Question 8

Solve.
-The population of a small country increases according to the function B = 1,600,000e0.04t, where t is measured in years. How many people will the country have after 2 years?

Accepted Answer

A)  1,923,623 
B)  1,755,056 
C)  4,041,166 
D)  1,733,259 
A)  1,923,623 
B)  1,755,056 
C)  4,041,166 
D)  1,733,259

Question 9

Expand. Assume that all variables represent positive real numbers.
-$\log _ { b } \left( \frac { x y ^ { 8 } } { z ^ { 7 } } \right)$

Accepted Answer

A)  $\log _ { b } x + \log _ { b } y ^ { 8 } - \log _ { b } z ^ { 7 }$ 
B)  $\log _ { \mathrm { b } } x + 8 \log _ { \mathrm { b } } \mathrm { y } - 7 \log _ { \mathrm { b } } z$ 
C)  $\log _ { b } x + 8 \log _ { b } y + 7 \log _ { b } z$ 
D)  $\log _ { b } x + \log _ { b } y ^ { 8 } + \log _ { b } z ^ { 7 }$ 
A)  $\log _ { b } x + \log _ { b } y ^ { 8 } - \log _ { b } z ^ { 7 }$ 
B)  $\log _ { \mathrm { b } } x + 8 \log _ { \mathrm { b } } \mathrm { y } - 7 \log _ { \mathrm { b } } z$ 
C)  $\log _ { b } x + 8 \log _ { b } y + 7 \log _ { b } z$ 
D)  $\log _ { b } x + \log _ { b } y ^ { 8 } + \log _ { b } z ^ { 7 }$

Question 10

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.
-$$f ( x ) = \log ( x + 5 ) + 3$$

Accepted Answer

A)  Vertical asymptote: $x = 5$;
Domain: $( 5 , \infty )$, Range: $( - \infty , \infty )$ 
B)  Vertical asymptote: $x = - 5$;
Domain: $( - 5 , \infty )$, Range: $( - \infty , \infty )$ 
C)  Vertical asymptote: $x = 0$;
Domain: $( - \infty , 0 )$, Range: $( 0 , \infty )$ 
D)  Vertical asymptote: $x = + 3$;
Domain: $( + 3 , \infty )$, Range: $( - \infty , \infty )$ 
A)  Vertical asymptote: $x = 5$;
Domain: $( 5 , \infty )$, Range: $( - \infty , \infty )$ 
B)  Vertical asymptote: $x = - 5$;
Domain: $( - 5 , \infty )$, Range: $( - \infty , \infty )$ 
C)  Vertical asymptote: $x = 0$;
Domain: $( - \infty , 0 )$, Range: $( 0 , \infty )$ 
D)  Vertical asymptote: $x = + 3$;
Domain: $( + 3 , \infty )$, Range: $( - \infty , \infty )$

Question 11

Rewrite in logarithmic form.
-$$5 ^ { 2 } = 25$$

Accepted Answer

A)  $\log _ { 5 } 2 = 25$ 
B)  $\log _ { 2 } 25 = 5$ 
C)  $\log _ { 5 } 25 = 2$ 
D)  $\log _ { 25 } 5 = 2$ 
A)  $\log _ { 5 } 2 = 25$ 
B)  $\log _ { 2 } 25 = 5$ 
C)  $\log _ { 5 } 25 = 2$ 
D)  $\log _ { 25 } 5 = 2$

Question 12

Rewrite as a single logarithm. Assume all variables represent positive real numbers.
-$2 \log _ { b } x - \log _ { b } y$

Accepted Answer

A)  $\log _ { b } x ^ { 2 } \div \log _ { b } y$ 
B)  $\log _ { b } \frac { x ^ { 2 } } { y }$ 
C)  $\log _ { b } \left( x ^ { 2 } - y \right)$ 
D)  $\log _ { b } \frac { 2 x } { y }$ 
A)  $\log _ { b } x ^ { 2 } \div \log _ { b } y$ 
B)  $\log _ { b } \frac { x ^ { 2 } } { y }$ 
C)  $\log _ { b } \left( x ^ { 2 } - y \right)$ 
D)  $\log _ { b } \frac { 2 x } { y }$

Question 13

Find all intercepts for the given function. Round to the nearest tenth if necessary.
-$$f ( x ) = \log ( x + 8 )$$

Accepted Answer

A)  $x$-int: $( - 7,0 )$; $y$-int: none 
B)  $x$-int: $( 8,0 ) ; y$-int: $( 0,0.9 )$ 
C)  $x$-int: none; $y$-int: $( 0,0.9 )$ 
D)  $x$-int: $( - 7,0 )$; $y$-int: $( 0,0.9 )$ 
A)  $x$-int: $( - 7,0 )$; $y$-int: none 
B)  $x$-int: $( 8,0 ) ; y$-int: $( 0,0.9 )$ 
C)  $x$-int: none; $y$-int: $( 0,0.9 )$ 
D)  $x$-int: $( - 7,0 )$; $y$-int: $( 0,0.9 )$

Question 14

Simplify.
-$5 ^ { \log _ { 5 } x }$

Accepted Answer

A)  $x$ 
B)  $- x$ 
C)  $5 x$ 
D)  $\frac { 1 } { x }$ 
A)  $x$ 
B)  $- x$ 
C)  $5 x$ 
D)  $\frac { 1 } { x }$

Question 15

Evaluate using the change-of-base formula. Round to four decimal places.
-$\log _ { 3 } 7$

Accepted Answer

A)  $- 1.7712$ 
B)  $3.5424$ 
C)  $1.7712$ 
D)  $0.5646$ 
A)  $- 1.7712$ 
B)  $3.5424$ 
C)  $1.7712$ 
D)  $0.5646$

Question 16

Simplify.
-$\log _ { 2 } 2 ^ { 2 }$

Accepted Answer

A)  $- 2$ 
B)  4 
C)  2 
D)  $- 4$ 
A)  $- 2$ 
B)  4 
C)  2 
D)  $- 4$

Question 17

Rewrite as a single logarithm. Assume all variables represent positive real numbers.
-$$( \log b x - \log b y ) + 6 \log b z$$

Accepted Answer

A)  $\log _ { b } \frac { x z ^ { 6 } } { y }$ 
B)  $\log _ { b } \frac { 6 x z } { y }$ 
C)  $\log _ { b } x z ^ { 6 } y$ 
D)  $\log _ { a } \frac { x } { z ^ { 6 } y }$ 
A)  $\log _ { b } \frac { x z ^ { 6 } } { y }$ 
B)  $\log _ { b } \frac { 6 x z } { y }$ 
C)  $\log _ { b } x z ^ { 6 } y$ 
D)  $\log _ { a } \frac { x } { z ^ { 6 } y }$

Question 18

Find all intercepts for the given function. Round to the nearest tenth if necessary.
-$$f ( x ) = \ln ( x + 6 ) - 2$$

Accepted Answer

A)  $x$-int: $( - 0.2,0 )$; $y$-int: $( 0,1.4 )$ 
B)  $x$-int: $( 1.4,0 )$; $y$-int: $( 0 , - 0.2 )$ 
C)  $x$-int: $( 1.4,0 )$; $y$-int: $( 0,4 )$ 
D)  $x$-int: $( - 6,0 ) ; y$-int: $( 0 , - 0.2 )$ 
A)  $x$-int: $( - 0.2,0 )$; $y$-int: $( 0,1.4 )$ 
B)  $x$-int: $( 1.4,0 )$; $y$-int: $( 0 , - 0.2 )$ 
C)  $x$-int: $( 1.4,0 )$; $y$-int: $( 0,4 )$ 
D)  $x$-int: $( - 6,0 ) ; y$-int: $( 0 , - 0.2 )$

Question 19

Simplify.
-$\ln e ^ { 6 }$

Accepted Answer

A)  $\frac { 1 } { 6 }$ 
B)  $\log 6$ 
C)  $- 6$ 
D)  6 
A)  $\frac { 1 } { 6 }$ 
B)  $\log 6$ 
C)  $- 6$ 
D)  6

Question 20

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.
-$$f ( x ) = \ln ( x - 1 ) + 3$$

Accepted Answer

A)  Vertical asymptote: $x = 3$;
Domain: $( 3 , \infty )$, Range: $( - \infty , \infty )$ 
B)  Vertical asymptote: $x = - 3$;
Domain: $( - \infty , - 3 )$, Range: $( - \infty , \infty )$ 
C)  Vertical asymptote: $x = 1$;
Domain: $( 1 , \infty )$, Range: $( - \infty , \infty )$ 
D)  Vertical asymptote: $x = 1$;
Domain: $( - \infty , 1 )$, Range: $( - \infty , \infty )$ 
A)  Vertical asymptote: $x = 3$;
Domain: $( 3 , \infty )$, Range: $( - \infty , \infty )$ 
B)  Vertical asymptote: $x = - 3$;
Domain: $( - \infty , - 3 )$, Range: $( - \infty , \infty )$ 
C)  Vertical asymptote: $x = 1$;
Domain: $( 1 , \infty )$, Range: $( - \infty , \infty )$ 
D)  Vertical asymptote: $x = 1$;
Domain: $( - \infty , 1 )$, Range: $( - \infty , \infty )$

Expand. Assume that all variables represent positive real numbers. - $\log _ { d } \left( \frac { a ^ { 7 } b ^ { 5 } } { c ^ { 3 } d ^ { 6 } } \right)$

Suppose for some base b > 0 (b ≠ 1) that logb 2 = A, logb 3 = B, logb 5 = C, and logb 7 = D. Express the given logarithms in terms of A, B, C, or D. - $\log _ { b } 6$

Suppose for some base b > 0 (b ≠ 1) that logb 2 = A, logb 3 = B, logb 5 = C, and logb 7 = D. Express the given logarithms in terms of A, B, C, or D. - $\log _ { b } 125$

Suppose for some base b > 0 (b ≠ 1) that logb 2 = A, logb 3 = B, logb 5 = C, and logb 7 = D. Express the given logarithms in terms of A, B, C, or D. - $\log _ { b } \left( \frac { 1 } { 125 } \right)$ A) $- 3 C$ B) $3 C$ C) $3 \mathrm { D }$ D) $- 3 \mathrm { D }$

Evaluate the given function. $Evaluate the given function. - f ( x ) = \log _ { 5 } x , f \left( \frac { 1 } { 25 } \right)$ $Evaluate the given function. - f ( x ) = \log _ { 5 } x , f \left( \frac { 1 } { 25 } \right)$ - $f ( x ) = \log _ { 5 } x , f \left( \frac { 1 } { 25 } \right)$

Evaluate using the change-of-base formula. Round to four decimal places. - $\log _ { 5 } 26.35$

Solve. -The number of acres in a landfill is given by the function B = 2800e-0.05t, where t is measured in years. How many acres will the landfill have after 2 years? (Round to the nearest acre.)

Solve. -The population of a small country increases according to the function B = 1,600,000e0.04t, where t is measured in years. How many people will the country have after 2 years?

Expand. Assume that all variables represent positive real numbers. - $\log _ { b } \left( \frac { x y ^ { 8 } } { z ^ { 7 } } \right)$

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function. - $f ( x ) = \log ( x + 5 ) + 3$

Rewrite in logarithmic form. - $5 ^ { 2 } = 25$

Rewrite as a single logarithm. Assume all variables represent positive real numbers. - $2 \log _ { b } x - \log _ { b } y$

Find all intercepts for the given function. Round to the nearest tenth if necessary. - $f ( x ) = \log ( x + 8 )$

Simplify. - $5 ^ { \log _ { 5 } x }$

Evaluate using the change-of-base formula. Round to four decimal places. - $\log _ { 3 } 7$

Simplify. - $\log _ { 2 } 2 ^ { 2 }$

Rewrite as a single logarithm. Assume all variables represent positive real numbers. - $( \log b x - \log b y ) + 6 \log b z$

Find all intercepts for the given function. Round to the nearest tenth if necessary. - $f ( x ) = \ln ( x + 6 ) - 2$

Simplify. - $\ln e ^ { 6 }$

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function. - $f ( x ) = \ln ( x - 1 ) + 3$

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Exponents and Polynomials

Factoring and Quadratic Equations

Rational Expressions and Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 12: Logarithmic and Exponential Functions

Expand. Assume that all variables represent positive real numbers. - log⁡d(a7b5c3d6)\log _ { d } \left( \frac { a ^ { 7 } b ^ { 5 } } { c ^ { 3 } d ^ { 6 } } \right)logd​(c3d6a7b5​)

Suppose for some base b > 0 (b ≠ 1) that logb 2 = A, logb 3 = B, logb 5 = C, and logb 7 = D. Express the given logarithms in terms of A, B, C, or D. - log⁡b6\log _ { b } 6logb​6

Suppose for some base b > 0 (b ≠ 1) that logb 2 = A, logb 3 = B, logb 5 = C, and logb 7 = D. Express the given logarithms in terms of A, B, C, or D. - log⁡b125\log _ { b } 125logb​125

Evaluate the given function. - f(x)=log⁡5x,f(125)f ( x ) = \log _ { 5 } x , f \left( \frac { 1 } { 25 } \right)f(x)=log5​x,f(251​)

Evaluate using the change-of-base formula. Round to four decimal places. - log⁡526.35\log _ { 5 } 26.35log5​26.35