# Algebra II : Solving Exponential Equations

## Example Questions

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### Example Question #1 : Solving Exponential Equations

Solve the equation for .

Explanation:

Begin by recognizing that both sides of the equation have a root term of .

Using the power rule, we can set the exponents equal to each other.

### Example Question #1 : Solving Exponential Functions

Solve the equation for .

Explanation:

Begin by recognizing that both sides of the equation have the same root term, .

We can use the power rule to combine exponents.

Set the exponents equal to each other.

### Example Question #3 : Solving Exponential Equations

In 2009, the population of fish in a pond was 1,034. In 2013, it was 1,711.

Write an exponential growth function of the form  that could be used to model , the population of fish, in terms of , the number of years since 2009.

Explanation:

Solve for the values of and b:

In 2009,  and  (zero years since 2009). Plug this into the exponential equation form:

. Solve for  to get  .

In 2013,  and . Therefore,

or  .   Solve for  to get

.

Then the exponential growth function is

.

### 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.

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:

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.

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.

.

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