Splash Screen. Concept Product Property of Logarithms Example.

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Presentation transcript:

Splash Screen

Concept Product Property of Logarithms Example

Example: Change of Base Formula

Example: Inverse Property of logarithms

Example 1 Use the Product Property Use log 5 2 ≈ to approximate the value of log log = log 5 (5 3 ● 2)Replace 250 with 5 3 ● 2. = log log 5 2Product Property = 3 + log 5 2Inverse Property of Exponents and Logarithms ≈ or Replace log 5 2 with Answer: Thus, log is approximately

Example 1 A.–3.415 B C D Given log 2 3 ≈ , what is the approximate value of log 2 96?

Concept Quotient Property of Logarithms

Example 2 Quotient Property SCIENCE The pH of a substance is defined as the concentration of hydrogen ions [H + ] in moles. It is given by the formula pH =. Find the amount of hydrogen in a liter of acid rain that has a pH of 5.5.

Example 2 Quotient Property UnderstandThe formula for finding pH and the pH of the rain is given. PlanWrite the equation. Then, solve for [H + ]. Solve Original equation Quotient Property Substitute 5.5 for pH. log 10 1 = 0

Example 2 Quotient Property Simplify. Multiply each side by –1. Definition of logarithm Answer: There are 10 –5.5, or about , mole of hydrogen in a liter of this rain. H+H+ H+H+ H+H+

Example 2 Quotient Property 5.5= log 10 1 – log –5.5 Quotient Property ? 5.5= 0 – (–5.5)Simplify. ? 5.5= 5.5  pH = 5.5 ? H + = 10 –5.5 Check

Example 2 A mole B mole C mole D mole SCIENCE The pH of a substance is defined as the concentration of hydrogen ions [H + ] in moles. It is given by the formula pH = log10 Find the amount of hydrogen in a liter of milk that has a pH of 6.7.

Concept Power Property of Logarithms Example

Example 3 Power Property of Logarithms Given that log 5 6 ≈ , approximate the value of log log 5 216=log Replace 216 with 6 3. =3 log 5 6Power Property ≈3(1.1133) or Replace log 5 6 with Answer:

Example 3 A B C D Given that log 4 6 ≈ , what is the approximate value of log ?

Example 4 Solve Equations Using Properties of Logarithms Multiply each side by 5. Solve 4 log 2 x – log 2 5 = log Original equation Power Property Quotient Property Property of Equality for Logarithmic Functions x=5Take the 4th root of each side.

Example 4 Solve Equations Using Properties of Logarithms Answer: 5 4 log 2 x – log 2 5 = log Check Substitute each value into the original equation. ? 4 log 2 5 – log 2 5 = log log – log 2 5 = log ? log = log ? log = log  ?

Example 4 A.x = 4 B.x = 18 C.x = 32 D.x = 144 Solve 2 log 3 (x – 2) – log 3 6 = log

Homework p. 488 # 3 – 57 (x3)

End of the Lesson