I need to answer these problems and show work

Please answer all the questions showing as much work as possible. I need to be able to understand the work. Thank you

Multiple Choice Part: Circle your answer to each of the following You will receive full
credit for correct answers. There is no penalty for incorrect answers.
1. (4 points) Which of the following is equivalent to the logarithmic equation loga (x) = 2?
a. 2. = a
b. =a?
c. a” = 2
d. a= 22
2. (4 points) Which of the following is equivalent to the cxponential equation 24 = c?
a. 4-log(v)
b. 4 = log, (c)
c. c = log (4)
d. v = log (4)
3. (4 points) Which of the following is approximately equal to log 12(61)?
a. 0.604
b. 4.305
c. 65.830
d. 1.654
Non-Multiple Choice Part: The following questions are all short answer. You must
show your work when indicated. If no work is shown, no credit will be given.
1. (4 points) Select all of the following tables which represent y as a function of c and are one-
to-one
510 10
+ 8 11
#S
1
10 13
8 11
10
13
8
S
2. (4 points) For each of the following graphs, tell whether it represents y as a function of x and
whether it has an inverse.
True or False: The graph is a function:
True or False: If the graph is a function, does
it have an inverse function?
True or False: The graph is a function:
True or False: If the graph is a function, does
it have an inverse function?
4. (4 points) Select the following that is equivalent to the expression below.
8 log (w) – 3 log (p)
a. log2
8w
Зр
b. log2
w8
C.
log2 (8)
log2 (3p)
d. log2 (8w – 3p)
5. (4 points) Select the following that is equivalent to the expression below.
loga
xy
23
a. log2 () + 4 log (y) – 3 log (2)
b. log (2) + 4 log (y) + 3 log (2)
c. log (x) – log (4y) – log (32)
log (2). -4log (y)
d.
3 log (2)
6. (4 points) Select the solution(s) to the equation 24-4 = 8-0+3.
a. 13/4
b. 10/3
c. 7/2
d. No solutions
3. (4 points) Find 9-‘(x) if (-) = 130 +4. Show your work!
4
4. (4 points) Solve the equation for c a=
5+2c
Show your work!
5. (4 points) Solve the equation 73-4 = 11 for x. If there is no solutions, write DNE. Leave
answers in exact form. Show your work!
6. (4 points) Solve the equation ln(7x – 1) = ln(x) + In(2) for 2. If there is no solutions, write
DNE. Leave answers in exact form. Show your work!
7. (4 points) Solve for in the equation log(2x – 3) = 1. Leave your answers in exact form.
Show your work!
Non-Multiple Choice Part: The following questions are all short answer. You must
show your work when indicated. If no work is shown, no credit will be given.
1. (4 points) Select all of the following tables which represent y as a function of c and are one-
to-one
510 10
+ 8 11
#S
1
10 13
8 11
10
13
8
S
2. (4 points) For each of the following graphs, tell whether it represents y as a function of x and
whether it has an inverse.
True or False: The graph is a function:
True or False: If the graph is a function, does
it have an inverse function?
True or False: The graph is a function:
True or False: If the graph is a function, does
it have an inverse function?
4. (4 points) Select the following that is equivalent to the expression below.
8 log (w) – 3 log (p)
a. log2
8w
Зр
b. log2
w8
C.
log2 (8)
log2 (3p)
d. log2 (8w – 3p)
5. (4 points) Select the following that is equivalent to the expression below.
loga
xy
23
a. log2 () + 4 log (y) – 3 log (2)
b. log (2) + 4 log (y) + 3 log (2)
c. log (x) – log (4y) – log (32)
log (2). -4log (y)
d.
3 log (2)
6. (4 points) Select the solution(s) to the equation 24-4 = 8-0+3.
a. 13/4
b. 10/3
c. 7/2
d. No solutions
3. (4 points) Find 9-‘(x) if (-) = 130 +4. Show your work!
4
4. (4 points) Solve the equation for c a=
5+2c
Show your work!
5. (4 points) Solve the equation 73-4 = 11 for x. If there is no solutions, write DNE. Leave
answers in exact form. Show your work!
6. (4 points) Solve the equation ln(7x – 1) = ln(x) + In(2) for 2. If there is no solutions, write
DNE. Leave answers in exact form. Show your work!
7. (4 points) Solve for in the equation log(2x – 3) = 1. Leave your answers in exact form.
Show your work!
8. (6 points) Let f(x) = log, (2 + 1).
(a) (2 points) What is the vertical asymptote
of f?
(b) (2 points) Give two points on the graph
and plot them.
(e) (2 points) Use the blank graph on the
right to sketch the graph of S. Clearly
indicate on the graph the vertical asymp-
tote, x-intercept, and whether the graph
is increasing or decreasing.
9. (6 points) Let S (2) = 2(3)”.
(a) (2 points) What is the horizontal asymp-
tote of f?
(b) (2 points) Determine two points on the
graph and plot them.
(c) (2 points) Use the blank graph on the
right to sketch the graph off. Clearly in-
dicate on the graph the horizontal asymp-
tote and whether the graph is increasing
or decreasing