Algebra II : Solving and Graphing Exponential Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #14 : Solving Exponential Functions

Solve for .

Possible Answers:

Correct answer:

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 .

Possible Answers:

Correct answer:

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 .

Possible Answers:

Correct answer:

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 .

Possible Answers:

Correct answer:

Explanation:

 Add  on both sides.

 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 .

Possible Answers:

Correct answer:

Explanation:

 Add  on both sides.

 

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 .

Possible Answers:

All real numbers

Correct answer:

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 .

Possible Answers:

Correct answer:

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 .

Possible Answers:

Correct answer:

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 .

Possible Answers:

Correct answer:

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 .

Possible Answers:

Correct answer:

Explanation:

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

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