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Ch. 8 Logarithmic Functions

Lesson 3 Laws of Logarithms

Warm-up: Evaluate or solve the following:

a) [pic] b) [pic] c) [pic]

Laws of Logarithms

Multiplication Law: [pic] = [pic] or [pic] = [pic]

Division Law: [pic] = [pic] or [pic] = [pic]

Power Law: [pic] = [pic] or [pic] = [pic]

Ex. Simplify the following into a single logarithmic form.

a) log 5 + log 12 b) log6 10 + log6 18 – log6 5

c) log a + log b – log c + log d d) 2 log4 x – log4 (x + 3)

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Ex. Write as a single logarithm.

a) [pic] b) [pic]

Ex. Evaluate.

a) [pic] b) [pic]

Ex. If [pic] and [pic] , evaluate [pic].

Ex. If log 2 = [pic] & log 3 = [pic] , express the following in terms of [pic] & [pic].

a) log 72 b) log 600

Change of Base:

[pic] where n is any base ([pic] & [pic])

Ex. Evaluate each logarithm to 3 decimal places using technology.

a) [pic] b) [pic]

Ex. The pH scale is used to measure the acidity or alkalinity of a solution. The pH of a solution is defined as pH = -log[H+], where [H+] is the hydrogen ion concentration in mol/L. A neutral solution, such as water, has a pH of 7, acids have pH < 7, and bases have pH > 7.

a) If cola has a pH of 2.5, how much more acidic is it than water?

b) An apple is 5 times as acidic as a pear. If a pear has a pH of 3.8, then what is the pH of an apple?

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