Algebra II : Solving and Graphing Exponential Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

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:

Addto 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:

Subtractfrom 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 convertto base.

We know the following:

Simplify.

Solve.

Example Question #10 :Solving Exponential Equations

Solve for.

Possible Answers:

Correct answer:

Explanation:

Let's convertto base.

We know the following:

Simplify.

Solve.

.

Example Question #11 :Solving Exponential Equations

Solve for.

Possible Answers:

Correct answer:

Explanation:

When multiplying exponents with the same base, we will apply the power rule of exponents:

We will simply add the exponents and keep the base the same.

Example Question #12 :Solving Exponential Equations

Solve for.

Possible Answers:

Correct answer:

Explanation:

When multiplying exponents with the same base, we will apply the power rule of exponents:

We will simply add the exponents and keep the base the same.

Simplify.

Solve.

Example Question #13 :Solving Exponential Equations

Solve for.

Possible Answers:

Correct answer:

Explanation:

When adding exponents with the same base, we need to see if we can factor out the numbers of the base.

我n 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.

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