Algebra II : Solving Exponential Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #51 : Solving Exponential Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents.

 With the same base, we can write:

 Take the square root on both sides and account for negative as well.

Example Question #52 : Solving Exponential Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents. We don't have the same base in this case, but we do know that . Therefore:

 Apply power rule of exponents.

 With the same base, we can now write:

 Take square root on both sides. Remember to account for negative.

 

Example Question #3831 : Algebra Ii

Solve for .

Possible Answers:

Correct answer:

Explanation:

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents. We don't have the same base in this case, but we do know that 

 Therefore:

 With the same base, we can now write

 Subtract  on both sides.

Example Question #3832 : Algebra Ii

Solve for .

Possible Answers:

Correct answer:

Explanation:

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents. We don't have the same base in this case, but we do know that 

 therefore

 With the same base, we can now write:

 Subtract  on both sides.

 Divide  on both sides.

Example Question #3833 : Algebra Ii

Solve for .

Possible Answers:

Correct answer:

Explanation:

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents. We don't have the same base in this case, but we do know that 

 and . By choosing base , we will have the same base and set-up an equation. 

 Apply power rule of exponents.

 With the same base, we can now write

 Subtract  on both sides.

 Divide  on both sides.

Example Question #3834 : Algebra Ii

Solve for .

Possible Answers:

Correct answer:

Explanation:

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents. We don't have the same base in this case, but we do know that 

 therefore

 Apply power rule of exponents.

 With the same base, we can now write

 Subtract  and add  on both sides.

 Divide  on both sides.

Example Question #3835 : Algebra Ii

Solve for .

Possible Answers:

Correct answer:

Explanation:

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents. We don't have the same base in this case, but we do know that 

 therefore

 With the same base, we can now write

 Subtract  on both sides.

 Divide  on both sides.

Example Question #3836 : Algebra Ii

Solve for .

Possible Answers:

Correct answer:

Explanation:

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents. We don't have the same base in this case, but we do know that 

 therefore

 With the same base, we now have

 Subtract  on both sides.

 Divide  on both sides.

Example Question #3837 : Algebra Ii

Solve for .

Possible Answers:

Correct answer:

Explanation:

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents. We don't have the same base in this case, but we do know that 

 By having a base of , this will make solving equations easier.

 Apply power rule of exponents.

 With the same base, we now can write

 Add  and subtract  on both sides.

 Divide  on both sides.

Example Question #3838 : Algebra Ii

Solve for .

Possible Answers:

Correct answer:

Explanation:

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents. We don't have the same base in this case, but we do know that 

 therefore

 Apply power rule of exponents.

 With the same base,  we can now write

 Add  and subtract  on both sides.

 Divide  on both sides.

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