Chapter 9 Section 5 Exponential and Logarithmic Equations

Chapter 9, Section 5 Exponential and Logarithmic Equations Page 716

Definition: Exponential Equation containing a variable in the exponent. Example: • • •

Solve: Expression Each Side has Same Base If 1) Rewrite with the same base 2) Set Exponents equal 3) Solve for the variable

Example Solve the equation: Solution: Rewrite with same base: Since: Equation becomes: Thus, 2 x = 5 And x =

Try Solve the equation: a) b)

Using Logarithms to Solve Exponential Equations • Isolate the exponential expression • Take the common or natural logarithm on both sides of the equation • Simplify by using the properties. • Solve for the variable.

Example • Solve the equation: • Solution: • Pick your base and take the logarithm of both sides. • Use the power rule. • Solve for x:

Try a) b)

Definition: Logarithmic Equations containing a variable in a logarithmic expression. Example: • ln (x + 2) = ln x •

Solve Logarithmic Equations • Express the equation in the form: • Use the definition of a logarithm to rewrite the equation in exponential form. • Solve for the variable • Check proposed solutions with original equation. Note: M > 0

Example Solve: Solution: • Rewrite in Exponential form: • Solve the equation

Try Solve the equations: a) b)

Summary • Exponential Equations • Same base • Different base • Logarithmic Equations • Isolate the logarithm • Use the definition of the logarithm • Solve