# Algebra II : Solving Exponential Equations

## Example Questions

### 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.

### Example Question #14 : Solving Exponential Functions

Solve for .

Explanation:

First, we need to convert  to base .

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.

### Example Question #11 : Solving Exponential Equations

Solve for .

Explanation:

When we add exponents, we try to factor to see if we can simplify it. Let's factor . We get . Remember to apply the rule of multiplying exponents which is to add the exponents and keeping the base the same.

With the same base, we can rewrite as .

### Example Question #12 : Solving Exponential Equations

Solve for .

Explanation:

When we add exponents, we try to factor to see if we can simplify it. Let's factor . We get . Remember to apply the rule of multiplying exponents which is to add the exponents and keeping the base the same.

With the same base, we can rewrite as .

### Example Question #13 : Solving Exponential Equations

Solve for .

Explanation:

When we add exponents, we try to factor to see if we can simplify it. Let's factor . We get . Remember to apply the rule of multiplying exponents which is to add the exponents and keeping the base the same.

With the same base, we can rewrite as .

### Example Question #14 : Solving Exponential Equations

Solve for .

Explanation:

When we add exponents, we try to factor to see if we can simplify it. Let's factor . We get . Remember to apply the rule of multiplying exponents which is to add the exponents and keeping the base the same.

With the same base, we can rewrite as .

### Example Question #15 : Solving Exponential Equations

Solve for .

All real numbers

Explanation:

When multiplying exponents with the same base, we add the exponents and keep the base the same.

We can just rewrite as such:

Solve for .