Solving Exponential and Logarithmic Functions Section 3 4

Solving Exponential and Logarithmic Functions Section 3. 4

Objective Solve exponential and logarithmic equations.

Relevance Learn how to evaluate data from real world applications that fit into an exponential or logarithmic model.

2 Basic Strategies for Solving Exponential & Log Equations One-To-One Properties l Inverse Properties l

Practice: Solve the equations and determine the property used. l

Solve l l

Solve l l

Solve l l

Solve l l

Solve l l

Solve l l

Solve l l

Solve l

Properties of Logarithms Section 3. 3

Properties of Logarithms

Simplify: (Condense)

Condense:

Condense:

Condense:

Condense:

Condense:

Condense:

Condense:

Condense:

Condense and Evaluate if Possible:

Expand:

Expand:

Expand:

Expand:

Solve Logarithms Section 3. 3

Solve:

Solve:

Extraneous Solutions Domain Restrictions!

Solve:

Solve:

Solve:

Solve By Substitution Section 3. 3

What Do You Think?

Solve by Using Substitution

Solve by Using Substitution

Common Logarithm

The Common Logarithm l l l The base-10 logarithm is called the common logarithm. The common logarithm is usually written as logx. If we can manage to make everything into log base 10, we can use our calculators to solve.

For Example…. Solve

Solve:

Solve:

Solve:

Solve:

Change of Base Section 3. 3 Solving with Unlike Bases

Change of Base l There is a way to write equivalent logarithmic expressions with different bases. l There is a formula to find the change of base. l Let’s derive the change of base formula…. .

Let’s derive the change of Base Formula!

Change of Base Formula:

Example: Evaluate to the nearest hundredth.

Practice (Nearest 100 th)

Practice (nearest 100 th)

Practice (Nearest 100 th)

Natural Log Equations

Practice (Nearest 100 th)

Practice (Nearest 100 th)

Practice (Nearest 100 th)

Practice (Nearest 100 th)