Algebra II : Mathematical Relationships and Basic Graphs
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Example Questions
Example Question #2 : Solving Exponential Functions
Solve for 
No solution
Because both sides of the equation have the same base, set the terms equal to each other.
Add 9 to both sides:
Then, subtract 2x from both sides:
Finally, divide both sides by 3:
Example Question #11 : Solving Functions
Solve for 
No solution
125 and 25 are both powers of 5.
Therefore, the equation can be rewritten as
Using the Distributive Property,
Since both sides now have the same base, set the two exponents equal to one another and solve:
Add 30 to both sides:
Add 
Divide both sides by 20:
Example Question #7 : Solving Exponential Equations
Solve 
No solution
Both 27 and 9 are powers of 3, therefore the equation can be rewritten as
Using the Distributive Property,
Now that both sides have the same base, set the two exponenents equal and solve.
Add 12 to both sides:
Subtract 
Example Question #1 : Solving Exponential Equations
The first step in thist problem is divide both sides by three: 
Example Question #9 : Solving Exponential Equations
Solve for 
Let's convert 
We know the following:
Simplify.
Solve.
Example Question #10 : Solving Exponential Equations
Solve for 
Let's convert 
We know the following:
Simplify.
Solve.
Example Question #11 : Solving Exponential Equations
Solve for 
When multiplying exponents with the same base, we will apply the power rule of exponents:
We will simply add the exponents and keep the base the same.
Example Question #11 : Solving Exponential Functions
Solve for 
When multiplying exponents with the same base, we will apply the power rule of exponents:
We will simply add the exponents and keep the base the same.
Simplify.
Solve.
Example Question #13 : Solving Exponential Equations
Solve for 
When adding exponents with the same base, we need to see if we can factor out the numbers of the base.
In this case, let's factor out 
We get the following:
Since we are now multiplying with the same base, we get the following expression:
Now we have the same base and we just focus on the exponents.
The equation is now:
Solve.
Example Question #14 : Solving Exponential Equations
Solve for 
First, we need to convert 
We know 
Therefore we can write the following expression:
Next, when we add exponents of the same base, we need to see if we can factor out terms.
In this case, let's factor out 
We get the following:
Since we are now multiplying with the same base, we get the following expression:
Now we have the same base and we just focus on the exponents.
The equation is now:
Solve.
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