2
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)
.
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?
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.