Question 1

Rewrite in logarithmic form
-$6^{2}=36$

Accepted Answer

A)  $\log _{2} 36=6$ 
B)  $\log _{6} 2=36$ 
C)  $\log _{36} 6=2$ 
D)  $\log _{6} 36=2$ 
A)  $\log _{2} 36=6$ 
B)  $\log _{6} 2=36$ 
C)  $\log _{36} 6=2$ 
D)  $\log _{6} 36=2$

Question 2

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

Accepted Answer

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

Question 3

Suppose for some base $b>0(b \neq 1)$ that $\log _{b} 2=A, \log _{b} 3=B, \log _{b} 5=C$, and $\log _{b} 7=D$. Express the given logarithms in terms of A, B, C, or D.
-$\log _{b} 14$

Accepted Answer

A)  $\mathrm{A}+\mathrm{B}$ 
B)  $-14 \mathrm{~A}$ 
C)  $A+D$ 
D)  $14 \mathrm{~A}$ 
A)  $\mathrm{A}+\mathrm{B}$ 
B)  $-14 \mathrm{~A}$ 
C)  $A+D$ 
D)  $14 \mathrm{~A}$

Question 4

Solve..
-$\log _{6} x=-5$

Accepted Answer

A)  $\left\{\frac{1}{15,625}\right\}$ 
B)  $\left\{\frac{1}{7776}\right\}$ 
C)  $\{7776\}$ 
D)  $\{15,625\}$ 
A)  $\left\{\frac{1}{15,625}\right\}$ 
B)  $\left\{\frac{1}{7776}\right\}$ 
C)  $\{7776\}$ 
D)  $\{15,625\}$

Question 5

Use the horizontal-line test to determine whether the function is one to one.
-

Accepted Answer

A) True 
 B)False

Question 6

Rewrite using the power rule. Assume all variables represent positive real numbers.
-$\log _{2} y^{7}$

Accepted Answer

A)  $7 \log 2 y$ 
B)  $7 \log 2 \mathrm{y}$ 
C)  $\log _{2} 7 \mathrm{y}$ 
D)  $14 \log \mathrm{y}$ 
A)  $7 \log 2 y$ 
B)  $7 \log 2 \mathrm{y}$ 
C)  $\log _{2} 7 \mathrm{y}$ 
D)  $14 \log \mathrm{y}$

Question 7

For the given functions $f(x)$ and $g(x)$, find a value $x$ for which $(f\circ g)(x)=(g\circ f)(x)$.
-$f(x)=x^{2}+7 x-4, g(x)=x-6$

Accepted Answer

A)  $x=\frac{3}{2}$ 
B)  $x=0$ 
C)  $x=7$ 
D)  $x=-1$ 
A)  $x=\frac{3}{2}$ 
B)  $x=0$ 
C)  $x=7$ 
D)  $x=-1$

Question 8

Rewrite using the power rule. Assume all variables represent positive real numbers.
-$\log _{4} y^{8}$

Accepted Answer

A)  $8 \log _{4} \mathrm{y}$ 
B)  $8 \log _{4} y^{8}$ 
C)  $4 \log _{8} \mathrm{y}$ 
D)  $4 \log _{8} \mathrm{y}^{8}$ 
A)  $8 \log _{4} \mathrm{y}$ 
B)  $8 \log _{4} y^{8}$ 
C)  $4 \log _{8} \mathrm{y}$ 
D)  $4 \log _{8} \mathrm{y}^{8}$

Question 9

Solve.
-$\log _{2}(4 x+8)=\log _{2}(4 x+5)$

Accepted Answer

A)  $\{3\}$ 
B)  $\varnothing$ 
C)  $\{0\}$ 
D)  $\left\{\frac{13}{3}\right\}$ 
A)  $\{3\}$ 
B)  $\varnothing$ 
C)  $\{0\}$ 
D)  $\left\{\frac{13}{3}\right\}$

Question 10

For the given function $f(x)$, find $f^{-1}(x)$ and graph the function and its inverse.
-$f(x)=3^{x}$

Accepted Answer

A)  $ f(x)=3^{x}, f^{-1}(x)=\log _{3} x $
  
B)  $ f(x)=3^{x}, f^{-1}(x)=\log _{3} x $
  
C)  $ f(x)=3^{x}, f^{-1}(x)=x $
  
D)  $ f(x)=3^{x}, f^{-1}(x)=\log 3 x $
  
A)  $ f(x)=3^{x}, f^{-1}(x)=\log _{3} x $
  
B)  $ f(x)=3^{x}, f^{-1}(x)=\log _{3} x $
  
C)  $ f(x)=3^{x}, f^{-1}(x)=x $
  
D)  $ f(x)=3^{x}, f^{-1}(x)=\log 3 x $

Question 11

Given $f(x)$ and $g(x)$, find the indicated composition and evaluate.
-$f(x)=x-6 ; g(x)=-7 x^{2}-8 x-7$
Find (f $\circ \mathrm{g})(4)$.

Accepted Answer

A)  -2419 
B)  -408 
C)  -277 
D)  -912 
A)  -2419 
B)  -408 
C)  -277 
D)  -912

Question 12

Simplify.
-$\ln e^{4}$

Accepted Answer

A)  $\frac{1}{4}$ 
B)  $\log 4$ 
C)  4 
D)  - 4 
A)  $\frac{1}{4}$ 
B)  $\log 4$ 
C)  4 
D)  - 4

Question 13

Find the specified domain
-For $f(x)=3 \sqrt{x+5}$ and $g(x)=2 x+15$, what is the domain of $g$ of?

Accepted Answer

A)  $(-\infty, \infty)$ 
B)  $(-5, \infty)$ 
C)  $[-5, \infty)$ 
D)  $[-20, \infty)$ 
A)  $(-\infty, \infty)$ 
B)  $(-5, \infty)$ 
C)  $[-5, \infty)$ 
D)  $[-20, \infty)$

Question 14

A computer is purchased for $\$ 3200$. Its value each year is about $75 \%$ of the value the preceding year. Its value, in dollars, after $t$ years is given by the exponential function $V(t)=3200(0.75)^{t}$. Find the value of the computer after 10 years.

Accepted Answer

A)  $\$ 24,000.00$ 
B)  $\$ 135.15$ 
C)  $\$ 101.36$ 
D)  $\$ 180.20$ 
A)  $\$ 24,000.00$ 
B)  $\$ 135.15$ 
C)  $\$ 101.36$ 
D)  $\$ 180.20$

Question 15

Rewrite as a single logarithm using the product rule for logarithms. A ssume all variables represent positive real numbers.
-$\log _{4} 8+\log _{4} x$

Accepted Answer

A)  $\log _{32} x$ 
B)  $\log _{4} 8^{x}$ 
C)  $\log _{4}(x+8)$ 
D)  $\log _{4}(8 x)$ 
A)  $\log _{32} x$ 
B)  $\log _{4} 8^{x}$ 
C)  $\log _{4}(x+8)$ 
D)  $\log _{4}(8 x)$

Question 16

Rewrite using the pow er and product rules. Assume all variables represent positive real numbers.
-$\log _{a} 5 x^{4} y z^{6}$

Accepted Answer

A)  $\log _{a} 5+4 \log _{a} x+\log _{a} y+6 \log _{a} z$ 
B)  $24 \log _{a} 5 x y z$ 
C)  $5+\log _{\mathrm{a}} y+\log _{\mathrm{a}} \mathrm{z} 6$ 
D)  $\log _{a} 5-4 \log _{a} x-\log _{a} y-6 \log _{a} z$ 
A)  $\log _{a} 5+4 \log _{a} x+\log _{a} y+6 \log _{a} z$ 
B)  $24 \log _{a} 5 x y z$ 
C)  $5+\log _{\mathrm{a}} y+\log _{\mathrm{a}} \mathrm{z} 6$ 
D)  $\log _{a} 5-4 \log _{a} x-\log _{a} y-6 \log _{a} z$

Question 17

Solve the problem.
-A loan of $\$ 14,000$ is made at $12 \%$ interest, compounded annually. After tyears, the amount due, $A$, is given by the function
$$\mathrm{A}(\mathrm{t})=14,000(1.12)^{\mathrm{t}}$$
Find the doubling time. Round your answer to the nearest tenth.

Accepted Answer

A)  $6.1 \mathrm{yr}$ 
B)  $12.2 \mathrm{yr}$ 
C)  $17.6 \mathrm{yr}$ 
D)  $9.7 \mathrm{yr}$ 
A)  $6.1 \mathrm{yr}$ 
B)  $12.2 \mathrm{yr}$ 
C)  $17.6 \mathrm{yr}$ 
D)  $9.7 \mathrm{yr}$

Question 18

Suppose for some base $b>0(b \neq 1)$ that $\log _{b} 2=A, \log _{b} 3=B, \log _{b} 5=C$, and $\log _{b} 7=D$. Express the given logarithms in terms of A, B, C, or D.
-$\log _{b} 25$

Accepted Answer

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

Question 19

For the given functions $f(x)$ and $g(x)$, find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.
-$f(x)=x+4, g(x)=x+7$
Find $(f \cdot g)(x)$.

Accepted Answer

A)  $x^{2}+11 x+11$ 
B)  $x^{2}+8 x+28$ 
C)  $x^{2}+11 x+28$ 
D)  $x^{2}+28$ 
A)  $x^{2}+11 x+11$ 
B)  $x^{2}+8 x+28$ 
C)  $x^{2}+11 x+28$ 
D)  $x^{2}+28$

Question 20

Use the horizontal-line test to determine whether the function is one to one.
-

Accepted Answer

A) True 
 B)False

Rewrite in logarithmic form - $6^{2}=36$

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

Suppose for some base $b>0(b \neq 1)$ that $\log _{b} 2=A, \log _{b} 3=B, \log _{b} 5=C$ , and $\log _{b} 7=D$ . Express the given logarithms in terms of A, B, C, or D. - $\log _{b} 14$

Solve.. - $\log _{6} x=-5$

Use the horizontal-line test to determine whether the function is one to one. -

Rewrite using the power rule. Assume all variables represent positive real numbers. - $\log _{2} y^{7}$

For the given functions $f(x)$ and $g(x)$ , find a value $x$ for which $(f\circ g)(x)=(g\circ f)(x)$ . - $f(x)=x^{2}+7 x-4, g(x)=x-6$

Rewrite using the power rule. Assume all variables represent positive real numbers. - $\log _{4} y^{8}$

Solve. - $\log _{2}(4 x+8)=\log _{2}(4 x+5)$

For the given function $f(x)$ , find $f^{-1}(x)$ and graph the function and its inverse. - $f(x)=3^{x}$ $For the given function f(x) , find f^{-1}(x) and graph the function and its inverse. - f(x)=3^{x}$

Given $f(x)$ and $g(x)$ , find the indicated composition and evaluate. - $f(x)=x-6 ; g(x)=-7 x^{2}-8 x-7$ Find (f $\circ \mathrm{g})(4)$ .

Simplify. - $\ln e^{4}$

Find the specified domain -For $f(x)=3 \sqrt{x+5}$ and $g(x)=2 x+15$ , what is the domain of $g$ of?

A computer is purchased for $\$ 3200$ . Its value each year is about $75 \%$ of the value the preceding year. Its value, in dollars, after $t$ years is given by the exponential function $V(t)=3200(0.75)^{t}$ . Find the value of the computer after 10 years.

Rewrite as a single logarithm using the product rule for logarithms. A ssume all variables represent positive real numbers. - $\log _{4} 8+\log _{4} x$

Rewrite using the pow er and product rules. Assume all variables represent positive real numbers. - $\log _{a} 5 x^{4} y z^{6}$

Solve the problem. -A loan of $\$ 14,000$ is made at $12 \%$ interest, compounded annually. After tyears, the amount due, $A$ , is given by the function $\mathrm{A}(\mathrm{t})=14,000(1.12)^{\mathrm{t}}$ Find the doubling time. Round your answer to the nearest tenth.

Suppose for some base $b>0(b \neq 1)$ that $\log _{b} 2=A, \log _{b} 3=B, \log _{b} 5=C$ , and $\log _{b} 7=D$ . Express the given logarithms in terms of A, B, C, or D. - $\log _{b} 25$

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f(x)=x+4, g(x)=x+7$ Find $(f \cdot g)(x)$ .

Use the horizontal-line test to determine whether the function is one to one. -

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 9: Logarithmic and Exponential Functions

Rewrite in logarithmic form - 62=366^{2}=3662=36

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

Solve.. - log⁡6x=−5\log _{6} x=-5log6​x=−5

Use the horizontal-line test to determine whether the function is one to one. -

Rewrite using the power rule. Assume all variables represent positive real numbers. - log⁡2y7\log _{2} y^{7}log2​y7

For the given functions f(x)f(x)f(x) and g(x)g(x)g(x) , find a value xxx for which (f∘g)(x)=(g∘f)(x)(f\circ g)(x)=(g\circ f)(x)(f∘g)(x)=(g∘f)(x) . - f(x)=x2+7x−4,g(x)=x−6f(x)=x^{2}+7 x-4, g(x)=x-6f(x)=x2+7x−4,g(x)=x−6

Rewrite using the power rule. Assume all variables represent positive real numbers. - log⁡4y8\log _{4} y^{8}log4​y8

Solve. - log⁡2(4x+8)=log⁡2(4x+5)\log _{2}(4 x+8)=\log _{2}(4 x+5)log2​(4x+8)=log2​(4x+5)

For the given function f(x)f(x)f(x) , find f−1(x)f^{-1}(x)f−1(x) and graph the function and its inverse. - f(x)=3xf(x)=3^{x}f(x)=3x

Given f(x)f(x)f(x) and g(x)g(x)g(x) , find the indicated composition and evaluate. - f(x)=x−6;g(x)=−7x2−8x−7f(x)=x-6 ; g(x)=-7 x^{2}-8 x-7f(x)=x−6;g(x)=−7x2−8x−7 Find (f ∘g)(4)\circ \mathrm{g})(4)∘g)(4) .

Simplify. - ln⁡e4\ln e^{4}lne4

Find the specified domain -For f(x)=3x+5f(x)=3 \sqrt{x+5}f(x)=3x+5​ and g(x)=2x+15g(x)=2 x+15g(x)=2x+15 , what is the domain of ggg of?

A computer is purchased for $3200\$ 3200$3200 . Its value each year is about 75%75 \%75% of the value the preceding year. Its value, in dollars, after ttt years is given by the exponential function V(t)=3200(0.75)tV(t)=3200(0.75)^{t}V(t)=3200(0.75)t . Find the value of the computer after 10 years.

Rewrite as a single logarithm using the product rule for logarithms. A ssume all variables represent positive real numbers. - log⁡48+log⁡4x\log _{4} 8+\log _{4} xlog4​8+log4​x

Rewrite using the pow er and product rules. Assume all variables represent positive real numbers. - log⁡a5x4yz6\log _{a} 5 x^{4} y z^{6}loga​5x4yz6

For the given functions f(x)f(x)f(x) and g(x)g(x)g(x) , find (f⋅g)(x)(f \cdot g)(x)(f⋅g)(x) or (fg)(x)\left(\frac{f}{g}\right)(x)(gf​)(x) as indicated. - f(x)=x+4,g(x)=x+7f(x)=x+4, g(x)=x+7f(x)=x+4,g(x)=x+7 Find (f⋅g)(x)(f \cdot g)(x)(f⋅g)(x) .

Use the horizontal-line test to determine whether the function is one to one. -

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Rewrite in logarithmic form - $6^{2}=36$

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

Solve.. - $\log _{6} x=-5$

Rewrite using the power rule. Assume all variables represent positive real numbers. - $\log _{2} y^{7}$

For the given functions $f(x)$ and $g(x)$ , find a value $x$ for which $(f\circ g)(x)=(g\circ f)(x)$ . - $f(x)=x^{2}+7 x-4, g(x)=x-6$

Rewrite using the power rule. Assume all variables represent positive real numbers. - $\log _{4} y^{8}$

Solve. - $\log _{2}(4 x+8)=\log _{2}(4 x+5)$

For the given function $f(x)$ , find $f^{-1}(x)$ and graph the function and its inverse. - $f(x)=3^{x}$ $For the given function f(x) , find f^{-1}(x) and graph the function and its inverse. - f(x)=3^{x}$

Given $f(x)$ and $g(x)$ , find the indicated composition and evaluate. - $f(x)=x-6 ; g(x)=-7 x^{2}-8 x-7$ Find (f $\circ \mathrm{g})(4)$ .

Simplify. - $\ln e^{4}$

Find the specified domain -For $f(x)=3 \sqrt{x+5}$ and $g(x)=2 x+15$ , what is the domain of $g$ of?

A computer is purchased for $\$ 3200$ . Its value each year is about $75 \%$ of the value the preceding year. Its value, in dollars, after $t$ years is given by the exponential function $V(t)=3200(0.75)^{t}$ . Find the value of the computer after 10 years.

Rewrite as a single logarithm using the product rule for logarithms. A ssume all variables represent positive real numbers. - $\log _{4} 8+\log _{4} x$

Rewrite using the pow er and product rules. Assume all variables represent positive real numbers. - $\log _{a} 5 x^{4} y z^{6}$

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f(x)=x+4, g(x)=x+7$ Find $(f \cdot g)(x)$ .