Unit 12 – Day 4 Name: Date: Integrated Math 4G: NOTES Logs and Exponents – Properties of Logs Properties of Logarithms:

Product Property:

Quotient Property:

Power Property:

Identity Property:

Expand using the properties of logarithms. Ex 1) log 3𝑥𝑦 Ex 2) log 25𝑥𝑦 Ex 3) log6

𝑥𝑧𝑦

Ex 4) log6𝑥

𝑦𝑧

Ex 5) log2𝑥4 Ex 6) log2

𝑥3

𝑦2 Ex 7) log55𝑥2 Ex 8) log2(𝑥𝑦)3

Unit 12 – Day 4

Product Property: log 𝑎𝑏 = log 𝑎 + log 𝑏 Quotient Property: log 𝑎𝑏

= log 𝑎 − log 𝑏

Power Property: log 𝑎𝑏 = 𝑏 log 𝑎 Identity Property: log𝑎𝑎 = 1 Condense using the properties of logarithms. Ex 9) 2log 𝑥 + 3log 𝑦 − 4log 𝑤 Ex 10) 4log3𝑥 − 8log3𝑦 Ex 11) 3log55 Ex 12) log54 + log4𝑥 Using the properties of logarithms to evaluate expressions: If log4𝑎 = 1, log4𝑏 = −2, and log4𝑐 = 3, evaluate the following: Ex 14) log4

𝑎𝑏𝑐

Ex 15) log4√𝑎𝑏𝑐 (hint: √☺ =☺12)

Ex 16) log4

𝑎3𝑏2

𝑐 Ex 17) log4

√𝑎𝑏𝑐

Unit 12 – Day 4 Name: Date: Integrated Math 4G: CLWK Logs and Exponents – Properties of Logs (#1-12) Expand using the properties of logarithms.

Unit 12 – Day 4 (#13-20) Condense using the properties of logarithms.

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