Algebra II : Solving and Graphing Exponential Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #62 : 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. However, since the base is different, we can definitely convert one of the numbers to have the same base. We know that 

 therefore

 With the same base, we now can write

 Add  on both sides.

 Divide  on both sides.

Example Question #63 : 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. However, since the base is different, we can definitely convert one of the numbers to have the same base. We know that 

 therefore

 With the same base, we can now write

 Add  on both sides.

 Divide  on both sides.

Example Question #64 : 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. However, since the base is different, we can definitely convert one of the numbers to have the same base. We know that 

 therefore

 With the same base, we can now write

 Add  on both sides.

 Divide  on both sides.

Example Question #65 : 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. However, since the base is different, we can definitely convert one of the numbers to have the same base. We know that 

 therefore

 Apply power rule of exponents.

 With the same base, we can now write

 Subtract  on both sides.

 Divide  on both sides.

Example Question #66 : 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. However, since the base is different, we can definitely convert one of the numbers to have the same base. We know that 

 therefore

 Apply the power rule of exponents.

 With the same base, we can now write

 Add  and subtract  on both sides.

 Divide  on both sides.

Example Question #67 : 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. However, since the base is different, we can definitely convert one of the numbers to have the same base. We know that 

 therefore

 Apply the power rule of exponents.

 With the same base, we can now write

 Add  and subtract  on both sides.

 Divide  on both sides.

Example Question #68 : 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. However, since the base is different, we can definitely convert one of the numbers to have the same base. We know that 

 therefore

 Apply the power rule of exponents.

 Add  and subtract  on both sides.

 Divide  on both sides.

Example Question #71 : 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. However, since the base is different, we can definitely convert one of the numbers to have the same base. We know that 

 therefore

 Apply the power rule of exponents.

 With the same base, we can now write

 Add  and subtract  on both sides.

Example Question #72 : 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. However, since the base is different, we can definitely convert one of the numbers to have the same base. We know that 

 therefore

 Apply the power rule of exponents.

 With the same base, we can now write

 Add  on both sides.

 

Example Question #73 : Solving Exponential Equations

Solve the equation:  

Possible Answers:

Correct answer:

Explanation:

Solve by first changing the base of the right side.

Rewrite the equation.

With common bases, we can set the powers equal to each other.

Use distribution to simplify the right side.

Add  on both sides.

Add two on both sides.

Divide by 9 on both sides.

The answer is:  

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