Exponential Equations

· An exponential equation is one in which a variable occurs in the exponent

https://cramster-image.s3.amazonaws.com/definitions/alg-14-eq-1.gif For example:

· https://cramster-image.s3.amazonaws.com/definitions/alg-14-eq-3.gif https://cramster-image.s3.amazonaws.com/definitions/alg-14-eq-2.gifWhen both sides of the equation have the same base, the exponents on either side are equal by the property if, then

Example 1. Solve for :

Solution:

Both sides of equations have same base so the exponents must be equals:

Example 2 . Solve for

Solution:

Since the base is not the same on both sides, we must make the same base

We know that: , replace with

Now that both sides of equations have the same base, take the exponents equal to each other

Example 3. Solve for

Solution:

Since the base is not the same on both sides, we must make the same base

We know that: , replace with

Now that both sides of equations have the same base, take the exponents equal to each other

Note: For all the questions, provide detailed solution steps.

Exercise 1. Solve the below equations for (100 points)

a) (10 points)

b) (20 Points)

c) (20 Points)

d) (10 points)

e) (20 points)

f) (20 points)