# Algebra II : Solving and Graphing Exponential Equations

## Example Questions

### 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:

### Example Question #16 : Solving Exponential Equations

Solve for .

Explanation:

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

We can just rewrite as such:

### Example Question #21 : Solving Exponential Equations

Solve for .

Explanation:

When dealing with exponents that are raised by another exponent, we multiply the exponents while keeping the base the same.

x

### Example Question #22 : Solving Exponential Equations

Solve for .

Explanation:

Although we don't have the same bases, we know . Therefore our equation is . Our equation is now .

Solve for .