Free Printable Exponential and Logs Test 1 Practice 2023-4

1.

Expand $\log\left(\frac{x}{y}\right)$

a)

logx+logy

b)

xlogy

c)

log(x-y)

d)

logx-logy

2.

Expand $\ln\left(\frac{2x^2y}{z^4}\right)$

a)

$\ln\left(2\right)+2\ln\left(x\right)+\ln\left(y\right)+4\ln\left(z\right)$

b)

$\ln\left(2\right)+2\ln\left(x\right)+\ln\left(y\right)-4\ln\left(z\right)$

c)

$2\ln\left(2xy\right)-4\ln\left(z\right)$

d)

$2\ln\left(2x\right)+\ln\left(y\right)-4\ln\left(z\right)$

3.

Expand log(4x³)

a)

log 4 + 3log x

b)

3log 4 + 3log x

c)

3log 4 + log x

d)

log 12 + log x

4.

Expand log_b(x/y)

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

5.

Semi-Annually means how many times a year?

a)

4

b)

2

c)

1

d)

6

6.

Riley invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Riley earn in 15 years?

a)

$1,584.62

b)

$2,651.39

c)

$2,706.86

d)

$1,825.10

7.

You want to save $5,000 for future family vacation. If you assume you can get an interest rate of 4.3% compounded monthly, then how much will you need to invest NOW to reach your vacation goal in 3 years?

a)

$307,042,791

b)

$5,000

c)

$3,250

d)

$4,395.89

8.

Tran invests $15,000 in a savings account that pays 4% simple interest. About how many years will it take for the account to double at this rate?

a)

7.22 years

b)

60.12 years

c)

17.67 years

d)

27.22 years

9.

Solve for x: log₆x + log₆(x-5) = 2

a)

√7

b)

9

c)

4

d)

none of these

10.

Solve:

log (x - 1) - log (x - 2) = log 5

a)

7

b)

4/9

c)

9/4

d)

1/7

11.

Solve:

ln(x+8) - ln (8) = 3

a)

152.68

b)

188.77

c)

4.24

d)

8.01

12.

Solve for x.
$\log_3\left(x-4\right)-\log_3\left(x\right)=1$

a)

-2

b)

0

c)

1

d)

No solution

13.

Sovle for x:
5^{-3x - 1} = 25

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

14.

Solve the equation for x.

a)

5.352

b)

4.326 E91

c)

2.324

d)

1.89

15.

Solve

a)

A

b)

B

c)

C

d)

D

16.

Solve 7ⁿ⁺¹⁰- 8 = 6

a)

-7.374

b)

-8.643

c)

-7.360

d)

-8.853

17.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

18.

a)

A

b)

B

c)

C

d)

D

19.

a)

A

b)

B

c)

C

d)

D

20.

Use multiple log properties to write as a single log:
log₂x - 5log₂y

a)

log₂(x/y⁵)

b)

log₂(xy⁵)

c)

log₂(x/y)⁵

d)

log₂(x/5y)

21.

a)

log (xy³)

b)

log (x⁶− y³)

c)

log (x⁶/y³)

d)

log (x⁶ + y³)

22.

a)

ln(wvu⁵)

b)

ln(u + v + w⁵)

c)

ln(uvw⁵)

d)

ln(uvw)⁵

23.

Expand: $\log_74\sqrt{d}$

(a)

Choose from the below words

$\log_7\ 4\ -\ \frac{1}{2}\log_7\ d$

$4\log_7d\ +\log_7\ \frac{1}{2}$

$\log_7\ 4+\frac{1}{2}\log_7\ d$

$\frac{1}{2}\log4d$

24.

Condense: $\log_9a\ +\ \frac{1}{2}\log_9b$

a)

$\log_9\ \frac{ab}{2}$

b)

$\log_9b\sqrt{a}$

c)

$\log_9a\sqrt{b}$

d)

$\log_9\ \frac{a}{\sqrt{b}}$

25.

Condense: $\log\ x\ -\left(3\log y+2\log z\right)$

a)

$\log\ \frac{x}{y^3z^2}$

b)

$\log\ xy^3z^2$

c)

$\log\ \frac{xy^3}{z^2}$

d)

$\log\ \frac{x}{5yz}$

26.

Condense: $4\ln p+2\ln q-3\ln r$

(a)

Choose from the below words

$\ln\ p^4q^2r^3$

$\ln\ \frac{p^4}{q^2r^3}$

$\ln\ \frac{8pq}{3r}$

$\ln\ \frac{p^4q^2}{r^3}$

27.

Willie and Anthony invest $8,515 in a retirement account with a fixed annual interest rate of 5% compounded continuously. What will the account balance be after 20 years?

a)

$22,017.32

b)

$23,146.17

c)

$20,021.95

d)

$20,943.52

28.

a)

3.39

b)

2.60

c)

2.58

d)

3.02

29.

Elizabeth invests $720 in a savings account with interest compounded at 3% monthly. She plans to save the money until it reaches the amount of $4500. How many years will it take her?

a)

t=59.800

b)

t=61.009

c)

t=138.011

d)

t=61.162

30.

Jane has a hard time waking up before she drinks a tall latte with 140 mg of caffeine. Each hour, the amount of caffeine in her system decreases by 13%. How long until she only has 26 mg of caffeine?

a)

t=17.066

b)

t=13.895

c)

t=12.089

d)

t=26.891

31.

On the second day, there were 40 bacteria in the petri dish and on the 7th day, there were 302 bacteria. Write an exponential power equation to model this growth.

a)

$y=17.82(1.50)^x$

b)

$y=17.82(1.50)x$

c)

$y=1.50\left(17.82\right)^x$

d)

$y=40.82(1.36)^x$

32.

On the fourth day, there were 16 lions in the jungle and on the 8th day, there were 27 lions. Write an exponential power equation to model this growth.

a)

$y=1.13(9.50)^x$

b)

$y=9.48(1.14)^x$

c)

$y=27\left(1.82\right)^x$

d)

$y=15.67(2.58)^x$

33.

Caiden earned $475 from mowing lawns last summer.He deposited this money in an account that pays an interest rate of 3.8% compounded annually. What will be his balance after 15 years?

a)

$827.52 (Mr. Williams)

b)

$831.10 (Mrs. Hoch)

c)

$839.45 (Mr. Krajunus)

d)

$846.80 (Ms. Palombo)

34.

Riley invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually,how much interest will Riley earn in 15 years?

a)

$1,584.62 the train station

b)

$1,651.39 the movie theater

c)

$1,706.86 the art museum

d)

$1,893.45 the bakery

35.

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

a)

$1,225,54

b)

$2,225.54

c)

$22,255.40

d)

$225.54

36.

Johnny takes an undisclosed sum of money and deposits it in a bank at an interest rate of 2%. He leaves the money in the account for 6 years, compounded quarterly. If the Johnny withdraws after 6 years is $455,125, what was the sum of money he deposited?

a)

$403 780

b)

$404 138

c)

$406 362

d)

$436 870

37.

If you are opening a savings account, is it better to have interest compounded daily or quarterly at 7%?

a)

Daily - so you earn money more often

b)

Quarterly - so you earn money less often

c)

who knows

d)

I need to consult my financial analyst

38.

Write an exponential function to model the situation. The value of a car is $18000 and is depreciating at a rate of 12% per year.

a)

V(t) = .88(18000)^t

b)

V(t) = .12(18000)^t

c)

V(t) = 18000(.88)^t

d)

V(t) = 18000(.12)^t

39.

Write an exponential function to model the situation. Then solve.

The value of a car is $18000 and is depreciating at a rate of 12% per year. What will the value of the car be after 10 years?

a)

V(t) = 18000(.88)^t ; $12986.98

b)

V(t) = 18000(.12)^t ; $12986.98

c)

V(t) = 18000(.88)^t ; $5013.02

d)

V(t) = 18000(.12)^t ; $5013.02

40.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

41.

Solve $\log_9\left(r-8\right)\ =\ 2$

a)

55

b)

$\frac{11}{6}$

c)

89

d)

6

42.

Solve $5\log_6\ \left(-5k\ -\ 9\right)\ +\ 2\ =\ 17$

a)

$-\frac{6571}{9}$

b)

-45

c)

$\frac{1}{5}$

d)

$\frac{3}{10}$

Exponential and Logs Test 1 Practice 2023-4

Total questions: 42

Worksheet time: 4hrs 26mins

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