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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

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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Example Question #24 : Solving Exponential Equations

Solve for .

$12^x\div12^{20}=12^{2x}$

Possible Answers:

Correct answer:

Explanation:

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

$12^x\div12^{20}=12^{x-20}=12^{2x}$

x-20=2x

x=-20

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Example Question #25 : Solving Exponential Equations

Solve for .

$2^x*4^{2x}=2^{60}$

Possible Answers:

Correct answer:

Explanation:

Although the bases are not the same, we know that 4=2^2 . Therefore we now have $2^x*4^{2x}=2^x*(2^2)^{2x}=2^x*2^{4x}=2^{60}$

Now, we can add the exponents. 5x=60

x=12

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Example Question #21 : Solving Exponential Equations

Solve for .

4^x+4^x=128

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 4^x(1+1)=4^x*2=128 . Remember to apply the rule of multiplying exponents which is to add the exponents and keeping the base the same. Next, we can divide on both sides.

4^x=64 We know 64=4^3

4^x=4^3 With the same base, we know that x=3 .

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Example Question #27 : Solving Exponential Equations

Solve $5^{4x}=125^{12}$ for .

Possible Answers:

$\frac{1}{9}$

$\frac{15}{4}$

Correct answer:

Explanation:

The first step in solving an equation like this to make the base the same on both sides of the equation. Since 5 is a factor of 125, we can rewrite the equation like this:

$5^{4x}=125^{12}$

$5^{4x}=(5^{3})^{12}$

Using the Power of a Power Property of exponents, we get:

$5^{4x}=5^{36}$

If the bases are the same on both sides of the equation, then the exponents must be equal, so

$5^{4x}=5^{36}$ becomes 4x=36

Solving for x:

x=9

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Example Question #28 : Solving Exponential Equations

Solve: $5^{3x-6} = 25^{9x-6}$

Possible Answers:

$\frac{2}{5}$

$\frac{4}{5}$

$\frac{5}{4}$

$\frac{3}{11}$

$\frac{1}{2}$

Correct answer:

$\frac{2}{5}$

Explanation:

In order to solve for the unknown variable, first change the base of the value of 25 to 5^2 .

The equation $5^{3x-6} = 25^{9x-6}$ becomes:

$5^{3x-6} = 5^{2(9x-6)}$

Since the bases are now the same, we can set the powers equal to each other.

3x-6 = 2(9x-6)

Simplify the right side by distributing the integer through the binomial.

3x-6 = 18x-12

Subtract from both sides.

3x-6 -3x= 18x-12-3x

-6= 15x-12

Add twelve on both sides.

-6+12= 15x-12+12

6=15x

Divide by fifteen on both sides and reduce the fraction.

$\frac{6}{15}=\frac{15x}{15}$

$x=\frac{6}{15} = \frac{2}{5}$

The answer is: $\frac{2}{5}$

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Example Question #3801 : Algebra Ii

Solve: $10^{2x-3} = 1000^{x}$

Possible Answers:

$\textup{The answer is not given.}$

$-\frac{6}{5}$

$-\frac{9}{11}$

Correct answer:

Explanation:

Rewrite the right side of the equation using a base of ten.

1000 = 10^3

One thousand to the power of x can be rewritten using the product of exponents.

$1000^{x} = (10^{3})^x$

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

Now that the bases are equal, set the powers equal to each other.

2x-3=3x

Subtract from both sides.

2x-3-2x=3x-2x

Simplify both sides.

-3=x

The answer is:

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Example Question #30 : Solving Exponential Equations

Solve the equation: $3^{3x} = 9^{x+3}$

Possible Answers:

$\frac{12}{25}$

$\frac{5}{6}$

$\frac{1}{6}$

Correct answer:

Explanation:

In order to solve this equation, we will need to convert the nine on the right side to a base of three.

9=3^2

Rewrite the equation.

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

Set the powers equal to each other since the bases are common.

3x= 2(x+3)

Distribute the two across the binomial.

3x=2x+6

Subtract from both sides.

3x-2x=2x+6-2x

x=6

The answer is:

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Example Question #32 : Solving And Graphing Exponential Equations

Solve the equation: $10^x = (\frac{1}{10})^{x+1}$

Possible Answers:

$\frac{1}{2}$

$\textup{There is no solution.}$

$-\frac{1}{2}$

$\frac{3}{4}$

$-\frac{1}{5}$

Correct answer:

$-\frac{1}{2}$

Explanation:

In order to determine the value of x, we will need to convert the base of one-tenth to the base of ten.

Rewrite the fraction as a base of ten.

$\frac{1}{10} = 10^{-1}$

Rewrite the right side of the equation using the new term.

$10^x = (10^{-1})^{x+1}$

According to the product rule for exponents, we can set the powers equal since the bases are similar.

x=-1(x+1)

Divide by negative one on both sides.

$\frac{x}{-1}=\frac{-1(x+1)}{-1}$

-x=x+1

Subtract on both sides. The equation will become:

-2x=1

Divide by negative two on both sides.

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

The answer is: $-\frac{1}{2}$

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Example Question #33 : Solving And Graphing Exponential Equations

Solve: $3^{6x-6}= 81^x$

Possible Answers:

$\frac{4}{3}$

$\textup{There is no solution.}$

$\frac{1}{3}$

Correct answer:

Explanation:

In order to solve this, we will need to rewrite the right side as the similar base to the left side of the equation.

81 = 3^4

Rewrite the right side.

$3^{6x-6}= (3^4)^x$

With similar bases, the powers can be set equal to each other.

6x-6 = 4x

Subtract on both sides.

6x-6 -(4x)= 4x-(4x)

2x-6 = 0

Add six on both sides.

2x-6 +6= 0+6

2x=6

Divide by two on both sides.

The answer is:

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #23 : Solving Exponential Equations

Example Question #24 : Solving Exponential Equations

Example Question #25 : Solving Exponential Equations

Example Question #21 : Solving Exponential Equations

Example Question #27 : Solving Exponential Equations

Example Question #28 : Solving Exponential Equations

Example Question #3801 : Algebra Ii

Example Question #30 : Solving Exponential Equations

Example Question #32 : Solving And Graphing Exponential Equations

Example Question #33 : Solving And Graphing Exponential Equations

All Algebra II Resources

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