Properties of Logarithms

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Presentation transcript:

Properties of Logarithms

Properties of Logarithms

Evaluate 1. 2. 3. 4.

Properties of Logarithms (contd.) 1. 2. 3.

Misconceptions log (a+b) NOT the same as log a + log b log (a * b) NOT same as (log a)(log b) log (a/b) NOT same as (log a)/(log b) log (1/a) NOT same as 1/(log a)

Basic properties of logarithms Fill in the missing values that make the equations below true: (a) (b) (c)

Change-of-Base Formula

For computation we use: For example:

Simplify: Simplify: Simplify: Simplify:

Rewrite the following as the sum/difference of logarithms with no exponents

Rewrite the following as the sum/difference of logarithms with no exponents

Rewrite the following as the sum/difference of logarithms with no exponents

Rewrite the following as the sum/difference of logarithms with no exponents

Rewrite the following as the sum/difference of logarithms with no exponents

Rewrite the following as the sum/difference of logarithms with no exponents

Rewrite the following as the sum/difference of logarithms with no exponents

Rewrite the following as a single logarithm:

Rewrite the following as a single logarithm:

Rewrite the following as a single logarithm:

Rewrite the following as a single logarithm:

Theorem

Solve

If ln 2 = a and ln 3 = b, find the following in terms of a and b: