Title: Exponential Equations

Very easy equation:

Example 1: Solve for x in the equation

Solution:

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

Solution:

Step 1: Take the natural logarithm of both sides:

Step 2: Use the rule .

Step 3: Find x:

Example 3:

Solve for x in the equation

Solution:

Step 1: Take the natural logarithm of both sides:

Step 2: Use the rule .

Step 3: Use the rule

Step 4: Find x

Example 4:

Solve for x in the equation

Solution:

Step 1:Isolate the exponential term

Step 2: Take the natural logarithm of both sides:

Step 3: Use the rule .

Step 4: Find x:

Example 5:

Solve for x in the equation

Solution:

Step 1:  Rewrite the equation in quadratic form:

Step 2: Factor the left side of the equation .

Step 3: Solve

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