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)
