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« Exponential Functions - Introductions
Exponential Functions: (lesson 2 of 3)

Exponential Equations

Very easy equation:

Example 1: Solve for x in the equation

Exponential Equation

Solution:

Solution of Exponential Equation

Not so easy equations:

It is often necessary to use a logarithm when solving an exponential equation.

Example 2:

Solve for x in the equation Exponential Equation

Solution:

Step 1: Take the natural logarithm of both sides:

Solution of Exponential Equation

Step 2: Use the rule Solution of Exponential Equation.

Solution of Exponential Equation

Step 3: Find x:

Solution of exponential Equation

Example 3:

Solve for x in the equation Example of Exponential Equation

Solution:

Step 1: Take the natural logarithm of both sides:

Solution of Exponential Equation

Step 2: Use the rule Solution of Exponential Equation.

Solution of Exponential Equation

Step 3: Use the rule Solution of Exponential Equation

Solution of Exponential Equation

Step 4: Find x

Solution of Exponential Equation

Example 4:

Solve for x in the equation Example of Exponential Equation

Solution:

Step 1:Isolate the exponential term

Solution of Exponential Equation

Step 2: Take the natural logarithm of both sides:

Solution of Exponential Equation

Step 3: Use the rule Solution of Exponential Equation.

Solution of Exponential Equation

Step 4: Find x:

Solution of Exponential Equation

Example 5:

Solve for x in the equation Example of Exponential Equation

Solution:

Step 1: Rewrite the equation in quadratic form:

Solution of Exponential Equation

Step 2: Factor the left side of the equation Solution of Exponential Equation.

Solution of Exponential Equation

Step 3: Solve Solution of Exponential Equation