# Algebra II : Solving Exponential Equations

## Example Questions

### 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 .

### Example Question #23 : Solving Exponential Equations

Solve for .

Explanation:

When dividing exponents with the same base, we just subtract the exponents and keep the base the same.

### Example Question #24 : Solving Exponential Equations

Solve for .

Explanation:

When dividing exponents with the same base, we just subtract the exponents and keep the base the same.

### Example Question #25 : Solving Exponential Equations

Solve for .

Explanation:

Although the bases are not the same, we know that . Therefore we now have

Now, we can add the exponents.

### Example Question #26 : 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. Next, we can divide  on both sides.

We know

With the same base, we know that .

### Example Question #27 : Solving Exponential Equations

Solve for .

Explanation:

The first step in solving an equation like this to make the base the same on both sides of the equation. Since 5 is a factor of 125, we can rewrite the equation like this:

Using the Power of a Power Property of exponents, we get:

If the bases are the same on both sides of the equation, then the exponents must be equal, so

becomes

Solving for x:

### Example Question #28 : Solving Exponential Equations

Solve:

Explanation:

In order to solve for the unknown variable, first change the base of the value of 25 to .

The equation  becomes:

Since the bases are now the same, we can set the powers equal to each other.

Simplify the right side by distributing the integer through the binomial.

Subtract  from both sides.

Divide by fifteen on both sides and reduce the fraction.

### Example Question #21 : Solving Exponential Equations

Solve:

Explanation:

Rewrite the right side of the equation using a base of ten.

One thousand to the power of x can be rewritten using the product of exponents.

Now that the bases are equal, set the powers equal to each other.

Subtract  from both sides.

Simplify both sides.

### Example Question #30 : Solving Exponential Equations

Solve the equation:

Explanation:

In order to solve this equation, we will need to convert the nine on the right side to a base of three.

Rewrite the equation.

Set the powers equal to each other since the bases are common.

Distribute the two across the binomial.

Subtract  from both sides.