Unit 12 Name: Date: Integrated Math 4G: HMWK

Unit 12: Logs and Exponents – Days 1-5 Homework

Day 1 Homework – Solving Exponential Equations Green Notes (#1-6) Simplify the following exponential expressions. 1) 3𝑥3 ∙ 2𝑥5 2) (3𝑥3)3 3) (4𝑥)−2 4) (2𝑥𝑦)2 ∙ (3𝑥3𝑦2)4 5) 3𝑥5 ∙ 2𝑥−2 6) 𝑥0 (#7-16) Solve the following exponential equations for 𝑥. 7) 32𝑥 = 9𝑥−1 8) 4𝑥 = 2𝑥2+1

9) 52𝑥 = 1625

10)

92𝑥+3 = 272𝑥−7 11) 26𝑥 = 16𝑥+3 12) 4𝑥+3 = 82𝑥−5

13)

34−𝑥 = 9𝑥+3

14) 42𝑥 = 164

15) 63𝑥 = 362𝑥−1 16) 25𝑥 = 322𝑥−1

Day 2 Homework – Solving Exponential Equations using Logarithms Yellow Notes (#1-11) Solve the following exponential equations using logarithms. Round all answers to the nearest hundredth. 1) 3𝑥 = 243 2) 5𝑥 = 3125

3) 2𝑥 = 164

4)

5𝑥 = 12.5 5) 32𝑥+1 = 47 6) 45−𝑥 = 122 7) 7𝑥−3 = 451 8) 82𝑥+1 = 72 9) 6𝑥+5 = 72 10) 122𝑥 = 189 11) 93𝑥−4 = 173

Unit 12

Day 3 Homework – Solving Simple Logarithmic and Exponential Equations Pink Notes (#1-6) Re-write each of the following in exponential form. 1) log636 = 2 2) log4256 = 4 3) log28 = 3

4) log39 = 2 5) log 1000 = 3 6) log3243 = 5 (#7-12) Re-write each of the following in logarithmic form. 7) 52 = 25 8) 21 = 2 9) 82 = 64

10) 102 = 100 11) 73 = 343 12) 122 = 144 (#13-18) Re-write in the opposite form.

13) 4−2 = 116

14) 2−5 = 132

15) 11−2 = 1121

16) log319

= −2 17) log51

125= −3 18) log 1

10000= −4

(#19-24) Solve the following logarithmic equations. 19) log7𝑥 = 2 20) log8𝑥 = 3 21) log96561 = 𝑥

22) log10100000 = 𝑥 23) log𝑥729 = 6 24) log𝑥216 = 3 (#25-30) Solve the following exponential equations. 25) 8𝑥 = 512 26) 𝑥3 = 64 27) 𝑥 = 103

28) 𝑦𝑥 = 𝑧 29) 11𝑥 = 1121

30) 𝑥−5 = 11024

(#31-34) Give an approximate value for 𝑥 rounded to the tenth. 31) 4𝑥 = 12 32) 2𝑥 = 40 33) log350 = 𝑥

34) log 500 = 𝑥

Unit 12

Day 4 Homework – Properties of Logs Blue Notes (#1-6) Write which property or properties of logarithms each equation demonstrates. Write “FALSE” if the equation is not true by the properties of logarithms. 1) log2𝑥 + log2𝑦 = log2𝑥𝑦 2) log440 = log42 + log45 3) log7

𝑥5

= 5log7𝑥 4) log9𝑥 − log9𝑦 = log7

𝑥𝑦 5) 6log6𝑥 = log6𝑥6 6) log 𝑥 + log2𝑦 = log 𝑥𝑦

(#7-10) Expand using the properties of logarithms.

7) log2𝑥𝑦𝑐

8) log 𝑎𝑏𝑐

9) log2𝑎2√𝑏 10) log3𝑎2𝑏4𝑐6𝑑8 (#11-14) Condense using the properties of logarithms.

11)

log2𝑎 + 2log2𝑏 − 3log2𝑐

12) 12

log 2 − 3log 3 13) log 5 − log 9 + log 3 14) log22 (#15-17) If log5𝑎 = 2, log5𝑏 = 4, and log5𝑐 = −1, evaluate the following.

15)

log5𝑎𝑏𝑐

16) log5𝑎

𝑏𝑐

17) log5𝑎√𝑏

𝑐

Day 5 Homework – Using the Properties of Logs and the Natural Log White Notes (#1-8) Solve for 𝑥. 1) log3𝑥 + log310 = 5 2) ln(10) = 𝑥 + 5

3) ln(𝑥2 − 4) − ln(𝑥 − 2) = 4 4) log4(2𝑥 + 9) + log43 = 2

5) 𝑒𝑥+2 = 13 6) 3𝑒2𝑥−1 = 15

7) 2ln(2𝑥 − 1) = 6 8) ln(3𝑥 + 4) = 3

Unit 12 – Day 1 Name: Date: Integrated Math 4G: HMWK Logs and Exponents – Solving Exponential Equations (#1-6) Simplify the following exponential expressions. 1) 3𝑥3 ∙ 2𝑥5 2) (3𝑥3)3

3) (4𝑥)−2 4) (2𝑥𝑦)2 ∙ (3𝑥3𝑦2)4

5) 3𝑥5 ∙ 2𝑥−2

6) 𝑥0

(#7-16) Solve the following exponential equations for 𝑥. 7) 32𝑥 = 9𝑥−1 8) 4𝑥 = 2𝑥2+1

Unit 12 – Day 1

9) 52𝑥 = 1625

10)

92𝑥+3 = 272𝑥−7

11) 26𝑥 = 16𝑥+3 12) 4𝑥+3 = 82𝑥−5

13)

34−𝑥 = 9𝑥+3

14) 42𝑥 = 164

15) 63𝑥 = 362𝑥−1 16) 25𝑥 = 322𝑥−1

Unit 12 – Day 2 Name: Date: Integrated Math 4G: HMWK Logs and Exponents – Solving Exponential Equations using Logarithms (#1-11) Solve the following exponential equations using logarithms. Round all answers to the nearest hundredth. 1) 3𝑥 = 243 2) 5𝑥 = 3125

3) 2𝑥 = 164

4)

5𝑥 = 12.5

5) 32𝑥+1 = 47 6) 45−𝑥 = 122

Unit 12 – Day 2 7) 7𝑥−3 = 451 8) 82𝑥+1 = 72

9) 6𝑥+5 = 72 10) 122𝑥 = 189

11) 93𝑥−4 = 173

Unit 12 – Day 3 Name: Date: Integrated Math 4G: HMWK Logs and Exponents – Solving Simple Logarithmic and Exponential Equations (#1-6) Re-write each of the following in exponential form. 1) log636 = 2 2) log4256 = 4 3) log28 = 3 4) log39 = 2 5) log 1000 = 3 6) log3243 = 5 (#7-12) Re-write each of the following in logarithmic form. 7) 52 = 25 8) 21 = 2 9) 82 = 64 10) 102 = 100 11) 73 = 343 12) 122 = 144 (#13-18) Re-write in the opposite form. 13) 4−2 = 1

16 14) 2−5 = 1

32

15) 11−2 = 1

121 16) log3

19

= −2

17) log5

1125

= −3 18) log 110000

= −4

Unit 12 – Day 3 (#19-24) Solve the following logarithmic equations. 19) log7𝑥 = 2 𝑥 =

20) log8𝑥 = 3 𝑥 =

21) log96561 = 𝑥 𝑥 =

22) log10100000 = 𝑥 𝑥 =

23) log𝑥729 = 6 𝑥 = 24) log𝑥216 = 3 𝑥 = (#25-30) Solve the following exponential equations. 25) 8𝑥 = 512 𝑥 =

26) 𝑥3 = 64 𝑥 =

27) 𝑥 = 103 𝑥 =

28) 𝑦𝑥 = 𝑧 𝑥 =

29) 11𝑥 = 1

121 𝑥 =

30) 𝑥−5 = 11024

𝑥 =

(#31-34) Give an approximate value for 𝑥 rounded to the tenth. 31) 4𝑥 = 12 𝑥 ≈ 32) 2𝑥 = 40 𝑥 ≈ 33) log350 = 𝑥 𝑥 ≈ 34) log 500 = 𝑥 𝑥 ≈

Unit 12 – Day 4 Name: Date: Integrated Math 4G: HMWK Logs and Exponents – Properties of Logs (#1-6) Write which property or properties of logarithms each equation demonstrates. Write “FALSE” if the equation is not true by the properties of logarithms. 1) log2𝑥 + log2𝑦 = log2𝑥𝑦 2) log440 = log42 + log45 3) log7

𝑥5

= 5log7𝑥 4) log9𝑥 − log9𝑦 = log7𝑥𝑦

5) 6log6𝑥 = log6𝑥6 6) log 𝑥 + log2𝑦 = log 𝑥𝑦 (#7-10) Expand using the properties of logarithms.

7) log2𝑥𝑦𝑐

8) log 𝑎𝑏𝑐

9) log2𝑎2√𝑏 10) log3𝑎2𝑏4𝑐6𝑑8

Unit 12 – Day 4 (#11-14) Condense using the properties of logarithms.

11)

log2𝑎 + 2log2𝑏 − 3log2𝑐

12) 12

log 2 − 3log 3

13) log 5 − log 9 + log 3 14) log22

(#15-17) If log5𝑎 = 2, log5𝑏 = 4, and log5𝑐 = −1, evaluate the following.

15)

log5𝑎𝑏𝑐

16) log5𝑎

𝑏𝑐

17) log5𝑎√𝑏

𝑐

Unit 12 – Day 5 Name: Date: Integrated Math 4G: HMWK Logs and Exponents – Using the Properties of Logs and the Natural Log (#1-8) Solve for 𝑥. 1) log3𝑥 + log310 = 5 2) ln(10) = 𝑥 + 5

3) ln(𝑥2 − 4) − ln(𝑥 − 2) = 4 4) log4(2𝑥 + 9) + log43 = 2

Unit 12 – Day 5 5) 𝑒𝑥+2 = 13 6) 3𝑒2𝑥−1 = 15

7) 2ln(2𝑥 − 1) = 6 8) ln(3𝑥 + 4) = 3