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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.