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Algebra II : Solving and Graphing Exponential Equations

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Example Question #14 : Solving Exponential Equations

Solve for .

3^x+3^x+3^x=27^2

Possible Answers:

$\frac{2}{3}$

$\frac{5}{3}$

Correct answer:

Explanation:

First, we need to convert 27^2 to base .

We know 27=3^3 .

Therefore we can write the following expression:

(3^3)^2=3^6 .

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 3^x .

We get the following:

3^x(1+1+1)=3^x(3) .

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

$3^{x+1}$ .

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

The equation is now:

x+1=6

Solve.

x=5

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Example Question #15 : Solving Exponential Equations

Solve for .

2^x+2^x=2^6

Possible Answers:

Correct answer:

Explanation:

When we add exponents, we try to factor to see if we can simplify it. Let's factor 2^x . We get $2^x(1+1)=2^x*2^1=2^{x+1}$ . Remember to apply the rule of multiplying exponents which is to add the exponents and keeping the base the same.

$2^{x+1}=2^6$ With the same base, we can rewrite as x+1=6 .

x=5

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Example Question #16 : Solving Exponential Equations

Solve for .

3^x+3^x+3^x=3^8

Possible Answers:

$\frac{8}{3}$

$\frac{7}{3}$

Correct answer:

Explanation:

When we add exponents, we try to factor to see if we can simplify it. Let's factor 3^x . We get $3^x(1+1+1)=3^x*3^1=3^{x+1}$ . Remember to apply the rule of multiplying exponents which is to add the exponents and keeping the base the same.

$3^{x+1}=3^8$ With the same base, we can rewrite as x+1=8 .

x=7

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Example Question #17 : Solving Exponential Equations

Solve for .

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

Possible Answers:

Correct answer:

Explanation:

$2^{10}-2^x=2^x$ Add 2^x on both sides.

$2^{10}=2^x+2^x$ When we add exponents, we try to factor to see if we can simplify it. Let's factor 2^x . We get $2^x(1+1)=2^x*2^1=2^{x+1}$ . Remember to apply the rule of multiplying exponents which is to add the exponents and keeping the base the same.

$2^{x+1}=2^{10}$ With the same base, we can rewrite as x+1=10 .

x=9

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Example Question #18 : Solving Exponential Equations

Solve for .

$2^{21}-2^{-x}=2^{-x}$

Possible Answers:

-10.5

10.5

Correct answer:

Explanation:

$2^{21}-2^{-x}=2^{-x}$ Add $2^{-x}$ on both sides.

$2^{21}=2^{-x}+2^{-x}$

When we add exponents, we try to factor to see if we can simplify it. Let's factor $2^{-x}$ . We get $2^{-x}(1+1)=2^{-x}*2^1=2^{-x+1}$ . Remember to apply the rule of multiplying exponents which is to add the exponents and keeping the base the same.

$2^{-x+1}=2^{21}$ With the same base, we can rewrite as -x+1=21 .

-x=20

x=-20

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Example Question #21 : Solving And Graphing Exponential Equations

Solve for .

$4^x*4^8=4^{2x}$

Possible Answers:

All real numbers

Correct answer:

Explanation:

$4^x*4^8=4^{2x}$ When multiplying exponents with the same base, we add the exponents and keep the base the same.

$4^{x+8}=4^{2x}$ We can just rewrite as such: x+8=2x

x=8

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Example Question #20 : Solving Exponential Equations

Solve for .

$6^x*6^8=6^{24}$

Possible Answers:

Correct answer:

Explanation:

$6^x*6^8=6^{24}$ When multiplying exponents with the same base, we add the exponents and keep the base the same.

$6^{x+8}=6^{24}$ We can just rewrite as such: x+8=24

x=16

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Example Question #21 : Solving Exponential Equations

Solve for .

$(7^8)^x=7^{72}$

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.

$(7^8)^x=7^{8x}=7^{72}$ 8x=72 x x=9

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Example Question #22 : Solving Exponential Equations

Solve for .

(5^x)^3=125^6

Possible Answers:

Correct answer:

Explanation:

Although we don't have the same bases, we know 125=5^3 . Therefore our equation is $(5^x)^3=(5^3)^6=5^{18}$ . Our equation is now 3x=18 .

x=6

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Example Question #23 : Solving Exponential Equations

Solve for .

$9^8\div9^x=9^{-3}$

Possible Answers:

Correct answer:

Explanation:

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

$9^8\div9^x=9^{8-x}=9^{-3}$

8-x=-3

x=11

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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 #14 : Solving Exponential Equations

Example Question #15 : Solving Exponential Equations

Example Question #16 : Solving Exponential Equations

Example Question #17 : Solving Exponential Equations

Example Question #18 : Solving Exponential Equations

Example Question #21 : Solving And Graphing Exponential Equations

Example Question #20 : Solving Exponential Equations

Example Question #21 : Solving Exponential Equations

Example Question #22 : Solving Exponential Equations

Example Question #23 : Solving Exponential Equations

All Algebra II Resources

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