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Algebra II : Exponents

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Example Questions

Example Question #75 : Solving Exponential Equations

Solve for $\displaystyle x$.

$7^{x+5}=7^{12}$ $\displaystyle 7^{x+5}=7^{12}$

Possible Answers:

$\displaystyle 7$

$\displaystyle 13$

$\displaystyle 6$

$\displaystyle 17$

$\displaystyle 8$

Correct answer:

$\displaystyle 7$

Explanation:

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents.

$7^{x+5}=7^{12}$ $\displaystyle 7^{x+5}=7^{12}$ With the same base, we can now write

x+5=12 $\displaystyle x+5=12$ Subtract $\displaystyle 5$ on both sides.

x=7 $\displaystyle x=7$

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Example Question #76 : Solving Exponential Equations

Solve for $\displaystyle x$.

$12^{x+4}=12^{8}$ $\displaystyle 12^{x+4}=12^{8}$

Possible Answers:

$\displaystyle 6$

$\displaystyle 8$

$\displaystyle 4$

$\displaystyle 12$

$\displaystyle 2$

Correct answer:

$\displaystyle 4$

Explanation:

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents.

$12^{x+4}=12^{8}$ $\displaystyle 12^{x+4}=12^{8}$ With the same base, we can now write

x+4=8 $\displaystyle x+4=8$ Subtract $\displaystyle 4$ on both sides.

x=4 $\displaystyle x=4$

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Example Question #77 : Solving Exponential Equations

Solve for $\displaystyle x$.

$14^{x+16}=14^{-13}$ $\displaystyle 14^{x+16}=14^{-13}$

Possible Answers:

$\displaystyle 3$

$\displaystyle 14$

$\displaystyle 19$

$\displaystyle -3$

$\displaystyle -29$

Correct answer:

$\displaystyle -29$

Explanation:

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents.

$14^{x+16}=14^{-13}$ $\displaystyle 14^{x+16}=14^{-13}$ With the same base, we can now write

$\displaystyle x+16=-13$ Subtract $\displaystyle 16$ on both sides.

x=-29 $\displaystyle x=-29$

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Example Question #78 : Solving Exponential Equations

Solve for $\displaystyle x$.

$12^{2x+17}=12^{-13}$ $\displaystyle 12^{2x+17}=12^{-13}$

Possible Answers:

$\displaystyle 12$

$\displaystyle -13$

$\displaystyle 11$

$\displaystyle -15$

$\displaystyle 14$

Correct answer:

$\displaystyle -15$

Explanation:

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents.

$12^{2x+17}=12^{-13}$ $\displaystyle 12^{2x+17}=12^{-13}$ With the same base, we can now write

$\displaystyle 2x+17=-13$ Subtract $\displaystyle 17$ on both sides.

2x=-30 $\displaystyle 2x=-30$ Divide $\displaystyle 2$ on both sides.

x=-15 $\displaystyle x=-15$

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Example Question #79 : Solving Exponential Equations

Solve for $\displaystyle x$.

$2^{3x+8}=4$ $\displaystyle 2^{3x+8}=4$

Possible Answers:

$\displaystyle -6$

$\displaystyle 5$

$\displaystyle 1$

$\displaystyle -2$

$\displaystyle 3$

Correct answer:

$\displaystyle -2$

Explanation:

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents. Since the bases are now different, we need to convert so we have the same base. We do know that

4=2^2 $\displaystyle 4=2^2$ therefore

$2^{3x+8}=2^2$ $\displaystyle 2^{3x+8}=2^2$ With the same base, we can now write

3x+8=2 $\displaystyle 3x+8=2$ Subtract $\displaystyle 8$ on both sides.

3x=-6 $\displaystyle 3x=-6$ Divide $\displaystyle 3$ on both sides.

x=-2 $\displaystyle x=-2$

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Example Question #80 : Solving Exponential Equations

Solve for $\displaystyle x$.

$3^{3x-6}=27$ $\displaystyle 3^{3x-6}=27$

Possible Answers:

$\displaystyle 6$

$\displaystyle 3$

$\displaystyle 5$

$\displaystyle 2$

$\displaystyle 4$

Correct answer:

$\displaystyle 3$

Explanation:

27=3^3 $\displaystyle 27=3^3$ therefore

$3^{3x-6}=3^3$ $\displaystyle 3^{3x-6}=3^3$ With the same base, we can now write

3x-6=3 $\displaystyle 3x-6=3$ Add $\displaystyle 6$ on both sides.

3x=9 $\displaystyle 3x=9$ Divide $\displaystyle 3$ on both sides.

x=3 $\displaystyle x=3$

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Example Question #81 : Solving And Graphing Exponential Equations

Solve for $\displaystyle x$.

$4^{2x-7}=64$ $\displaystyle 4^{2x-7}=64$

Possible Answers:

$\displaystyle 10$

$\displaystyle 7$

$\displaystyle 9$

$\displaystyle 3$

$\displaystyle 5$

Correct answer:

$\displaystyle 5$

Explanation:

64=4^3 $\displaystyle 64=4^3$ therefore

$4^{2x-7}=4^3$ $\displaystyle 4^{2x-7}=4^3$ With the same base, we can now write

2x-7=3 $\displaystyle 2x-7=3$ Add $\displaystyle 7$ on both sides.

2x=10 $\displaystyle 2x=10$ Divide $\displaystyle 2$ on both sides.

x=5 $\displaystyle x=5$

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Example Question #82 : Solving And Graphing Exponential Equations

Solve for $\displaystyle x$.

$7^{4x+8}=1$ $\displaystyle 7^{4x+8}=1$

Possible Answers:

$\displaystyle 1$

$\displaystyle -2$

$\displaystyle 3$

$\displaystyle -1$

$\displaystyle 0$

Correct answer:

$\displaystyle -2$

Explanation:

7^0=1 $\displaystyle 7^0=1$ therefore

$7^{4x+8}=7^0$ $\displaystyle 7^{4x+8}=7^0$ With the same base, we can now write

4x+8=0 $\displaystyle 4x+8=0$ Subtract $\displaystyle 8$ on both sides.

4x=-8 $\displaystyle 4x=-8$ Divide $\displaystyle 4$ on both sides.

x=-2 $\displaystyle x=-2$

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Example Question #83 : Solving And Graphing Exponential Equations

Solve for $\displaystyle x$.

$4^{2x+5}=8^{x}$ $\displaystyle 4^{2x+5}=8^{x}$

Possible Answers:

$\displaystyle 12$

$\displaystyle -5$

$\displaystyle 7$

$\displaystyle -9$

$\displaystyle -10$

Correct answer:

$\displaystyle -10$

Explanation:

$\displaystyle 4=2^2, 8=2^3$ therefore

$(2^2)^{2x+5}=(2^3)^{x}$ $\displaystyle (2^2)^{2x+5}=(2^3)^{x}$ Apply power rule of exponents.

$2^{4x+10}=2^{3x}$ $\displaystyle 2^{4x+10}=2^{3x}$ With the same base, we can now write

$\displaystyle 4x+10=3x$ Subtract $\displaystyle 4x$ on both sides.

10=-x $\displaystyle 10=-x$ Divide $\displaystyle -1$ on both sides.

-10=x $\displaystyle -10=x$

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Example Question #91 : Solving And Graphing Exponential Equations

Solve for $\displaystyle x$.

$25^{x+1}=125^{x+4}$ $\displaystyle 25^{x+1}=125^{x+4}$

Possible Answers:

$\displaystyle 9$

$\displaystyle 11$

$\displaystyle -5$

$\displaystyle -10$

$\displaystyle -8$

Correct answer:

$\displaystyle -10$

Explanation:

$\displaystyle 25=5^2, 125=5^3$ therefore

$(5^2)^{x+1}=(5^3)^{x+4}$ $\displaystyle (5^2)^{x+1}=(5^3)^{x+4}$ Apply power rule of exponents.

$5^{2x+2}=5^{3x+12}$ $\displaystyle 5^{2x+2}=5^{3x+12}$ With the same base, we can now write

$\displaystyle 2x+2=3x+12$ Subtract 2x, 12 $\displaystyle 2x, 12$ on both sides.

x=-10 $\displaystyle x=-10$

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Algebra II : Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #75 : Solving Exponential Equations

Example Question #76 : Solving Exponential Equations

Example Question #77 : Solving Exponential Equations

Example Question #78 : Solving Exponential Equations

Example Question #79 : Solving Exponential Equations

Example Question #80 : Solving Exponential Equations

Example Question #81 : Solving And Graphing Exponential Equations

Example Question #82 : Solving And Graphing Exponential Equations

Example Question #83 : Solving And Graphing Exponential Equations

Example Question #91 : Solving And Graphing Exponential Equations

All Algebra II Resources

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