Algebra 2

Chapter 7 Review

Exponential and Logarithmic Function

Exponential Parent Functions

Domain:

Range:

Asymptote:

Logarithmic Parent Functions

Domain:

Range:

Asymptote:

Key terms:

growth/decay factor

inverse functions

natural base e

asymptote

common logarithm

natural logarithm

exponentiation

logarithm with base b

Graph exponential and logarithmic functions.

1) 𝑦 =1

2(4)𝑥−1 + 3

a. Exponential growth or decay? How do you know?

b. Identify the asymptote and any transformations.

c. Graph the function. State the domain and range.

2) Graph the logarithmic function. State the domain, range, asymptote, and any

transformations. 𝑦 = −3𝑙𝑜𝑔4 (𝑥 + 2)

Solve these exponential equations.

3) 212𝑥 = 26𝑥+3 4) 274𝑥 = 3𝑥−5 5) 10𝑥−5 = 1003𝑥−7

Compound interest: 𝑨 = 𝑷 (𝟏 +𝒓

𝒏)

𝒏𝒕

Continuously compounded interest: 𝑨 = 𝑷𝒆𝒓𝒕

6) You put $7500 in a savings account paying 3% interest compounded. What is the

balance after 5 years if compounded: a) daily b) semi-annually c) weekly

7) Your grandparents put $500 in a savings account when you are born. The account

pays 4% interest continuously. When will the balance of the account double?

Rewrite the equation as a logarithm or in exponential form.

8) 𝑙𝑜𝑔3 81 = 4 9) 161

2 = 4

Evaluate the logarithm. No calculator.

10) 𝑙𝑜𝑔4 64 11) 𝑙𝑜𝑔 1 12) 𝑙𝑜𝑔91

3

13) 𝑙𝑜𝑔5 125 14) 𝑙𝑜𝑔5 1

25 15) 𝑙𝑜𝑔8 2

Solve these logarithmic equations.

16) 𝑙𝑜𝑔7 (6𝑥 − 10) = 𝑙𝑜𝑔7 (3𝑥 + 8) 17) 𝑙𝑜𝑔5 (𝑥2 − 4) = 𝑙𝑜𝑔5 (−𝑥 + 2)

Find the inverse.

18) 𝑦 = 𝑙𝑜𝑔 (𝑥 + 3) 19) 𝑦 = 8𝑥+1 − 4

Expand these expressions.

20) 𝑙𝑜𝑔 3𝑥

21) 𝑙𝑜𝑔 (2𝑥

9) 22) 𝑙𝑜𝑔 𝑧4

23) 𝑙𝑜𝑔 (𝑦5

𝑤)

Condense these expressions.

24) 5𝑙𝑜𝑔 9 − 𝑙𝑜𝑔 2 25) 𝑙𝑜𝑔6 2 + 2𝑙𝑜𝑔6 10 26) 8𝑙𝑜𝑔8 8

Solve these equations using the change of base formula. Round to three decimal

places if necessary.

27) 𝑙𝑜𝑔3 4 = 𝑥 28) 𝑙𝑜𝑔11 5 = 𝑥 29) 𝑙𝑜𝑔0.2 3 = 𝑥

Solve these equations.

30) 2 ln(𝑥 + 4) − 4 = 6 31) 1

3(4)𝑥 − 7 = 2

32) 8𝑒𝑥 = 96 33) 𝑙𝑜𝑔3 𝑥 + 𝑙𝑜𝑔3 (𝑥 − 8) = 2

34) 𝑙𝑜𝑔 𝑥 = 5 35) 𝑙𝑜𝑔4 (3𝑥 − 3) = 5

Simplify.

36) ln (𝑒−5)

37) (𝑒4)(𝑒−7)(𝑒2𝑥)

38) log5 125𝑥

39) log7 79𝑥

40) 5𝑒6

10𝑒2𝑥

41) (8𝑒9𝑥)1

3

Exponential Growth: 𝒚 = 𝒂(𝟏 + 𝒓)𝒕 Exponential Decay: 𝒚 = 𝒂(𝟏 − 𝒓)𝒕

42) You purchased a car for $15,000. Your car depreciates at a rate of 11% each year.

a. Write an exponential model to represent this data.

b. Using your model, calculate how much your car will cost in 5 years.

c. Using your model, calculate how old your car will be when it is worth $2,611.