Algebra II : Solving and Graphing Exponential Equations

Example Questions

Example Question #4 : Solving Exponential Equations

Solve for .

Explanation:

8 and 4 are both powers of 2.

Example Question #5 : Solving Exponential Equations

Solve for :

No solution

Explanation:

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 #6 : Solving Exponential Equations

Solve for :

No solution

Explanation:

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  to both sides:

Divide both sides by 20:

Example Question #7 : Solving Exponential Equations

Solve .

No solution

Explanation:

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  from both sides:

Example Question #8 : Solving Exponential Equations

Explanation:

The first step in thist problem is divide both sides by three: . Then, recognize that 8 could be rewritten with a base of 2 as well (). Therefore, your answer is 3.

Example Question #9 : Solving Exponential Equations

Solve for .

Explanation:

Let's convert  to base .

We know the following:

Simplify.

Solve.

Example Question #10 : Solving Exponential Equations

Solve for .

Explanation:

Let's convert  to base .

We know the following:

Simplify.

Solve.

.

Example Question #11 : Solving Exponential Functions

Solve for .

Explanation:

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 #12 : Solving Exponential Functions

Solve for .

Explanation:

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 Functions

Solve for .

Explanation:

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.