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Algebra II : Solving and Graphing Exponential Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #1 : Solving Exponential Functions

$4^{5x}=8^{4x-1}$

Solve for .

Possible Answers:

1.5

Correct answer:

1.5

Explanation:

8 and 4 are both powers of 2.

$4^{5x}=8^{4x-1}$

$2^{10x}=2^{12x-3}$

10x=12x-3 -2x=-3 x=1.5

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Example Question #2 : Solving Exponential Functions

Solve for :

$80^{2x+3}=80^{5x-9}$

Possible Answers:

x=80

$x=\frac{1}{4}$

x=2

x=4

No solution

Correct answer:

x=4

Explanation:

Because both sides of the equation have the same base, set the terms equal to each other.

2x+3=5x-9

Add 9 to both sides: 2x+12=5x

Then, subtract 2x from both sides: 12=3x

Finally, divide both sides by 3: x=4

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Example Question #11 : Solving Functions

Solve for :

$25^{-x+5}=125^{6x-10}$

Possible Answers:

$x=\frac{15}{7}$

x=5

No solution

x=2

$x=\frac{1}{2}$

Correct answer:

x=2

Explanation:

125 and 25 are both powers of 5.

Therefore, the equation can be rewritten as

$(5^3)^{6x-10}=(5^2)^{-x+5}$ .

Using the Distributive Property,

$5^{18x-30}=5^{-2x+10}$ .

Since both sides now have the same base, set the two exponents equal to one another and solve:

18x-30=-2x+10

Add 30 to both sides: 18x=-2x+40

Add to both sides: 20x=40

Divide both sides by 20: x=2

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Example Question #1 : Solving Exponential Equations

Solve $9^{4x+2}=27^{3x-4}$ .

Possible Answers:

No solution

x=16

x=6

$x=\frac{-16}{9}$

x=3

Correct answer:

x=16

Explanation:

Both 27 and 9 are powers of 3, therefore the equation can be rewritten as

$(3^2)^{4x+2}=(3^3)^{3x-4}$ .

Using the Distributive Property,

$3^{8x+4}=3^{9x-12}$ .

Now that both sides have the same base, set the two exponenents equal and solve.

8x+4=9x-12

Add 12 to both sides: 8x+16=9x

Subtract from both sides: 16=x

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Example Question #11 : Solving Functions

$(3)2^{x}=24$

Possible Answers:

x=-2

x=3

x=4

x=1

x=0

Correct answer:

x=3

Explanation:

The first step in thist problem is divide both sides by three: $2^{x}=8$ . Then, recognize that 8 could be rewritten with a base of 2 as well ( 2^3 ). Therefore, your answer is 3.

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Example Question #9 : Solving Exponential Equations

Solve for .

2^x=64

Possible Answers:

Correct answer:

Explanation:

Let's convert to base .

We know the following:

64=2*2*2*2*2*2

Simplify.

2*2*2*2*2*2=2^6

Solve.

x=6

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Example Question #10 : Solving Exponential Equations

Solve for .

3^x=2187

Possible Answers:

Correct answer:

Explanation:

Let's convert 2187 to base .

We know the following:

2187=3*3*3*3*3*3*3

Simplify.

3*3*3*3*3*3*3=3^7

Solve.

x=7 .

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Example Question #11 : Solving Exponential Equations

Solve for .

2^x*2^x=2^6

Possible Answers:

Correct answer:

Explanation:

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

(a^m)^n=a^m^n

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

2x=6

x=3

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Example Question #11 : Solving Exponential Functions

Solve for .

$3^7*3^{x+3}=3^{24}$

Possible Answers:

Correct answer:

Explanation:

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

(a^m)^n=a^m^n

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

7+x+3=24

Simplify.

10+x=24

Solve.

x=14

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Example Question #13 : Solving Exponential Equations

Solve for .

2^x+2^x=2^7

Possible Answers:

3.5

2.5

Correct answer:

Explanation:

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

In this case, let's factor out 2^x .

We get the following:

2^x(1+1)=2^x(2)

Since we are now multiplying with the same base, we get the following expression:

$2^{x+1}$

Now we have the same base and we just focus on the exponents.

The equation is now:

x+1=7

Solve.

x=6

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Algebra II : Solving and Graphing Exponential Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : Solving Exponential Functions

Example Question #2 : Solving Exponential Functions

Example Question #11 : Solving Functions

Example Question #1 : Solving Exponential Equations

Example Question #11 : Solving Functions

Example Question #9 : Solving Exponential Equations

Example Question #10 : Solving Exponential Equations

Example Question #11 : Solving Exponential Equations

Example Question #11 : Solving Exponential Functions

Example Question #13 : Solving Exponential Equations

All Algebra II Resources

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