Section 4-4
1
Math 150 Lecture Notes
Exponential and Logarithmic Equations
To Solve an Exponential Equation:
1. Isolate the exponential expression on one side of the equation.
2. Change from exponential to logarithmic form.
3. Use the Laws of Logarithms to solve for the variable.
To Solve a Logarithmic Equation:
1. Use the Laws of Logarithms to combine (condense) the logarithms into one term
2. Change from logarithmic to exponential form.
3. Solve the resulting equation for the variable.
Example 1: Find the solution of each exponential equation, correct to four decimal places.
2
3x
= 34 e
3-5x
= 16
2
1
10 =
+
−x
e
Example 2: Solve the equation.
x
2
e
x
+ xe
x
– e
x
= 0
