Algebra II : Solving Exponential Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #1 : Solving Exponential Equations

Solve the equation for .

Possible Answers:

Correct answer:

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 #2 : Solving Exponential Equations

Solve the equation for .

Possible Answers:

 

 

 

 

Correct answer:

 

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.

Possible Answers:

Correct answer:

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 .

Possible Answers:

Correct answer:

Explanation:

8 and 4 are both powers of 2.

Example Question #5 : Solving Exponential Equations

Solve for :

Possible Answers:

No solution

Correct answer:

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 :

Possible Answers:

No solution

Correct answer:

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 .

Possible Answers:

No solution

Correct answer:

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

Possible Answers:

Correct answer:

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 .

Possible Answers:

Correct answer:

Explanation:

Let's convert  to base .

We know the following:

Simplify.

Solve.

 

Example Question #10 : Solving Exponential Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

Let's convert  to base .

We know the following:

Simplify.

Solve.

.

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