Algebra II : Solving and Graphing Exponential Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #74 : Solving Exponential Equations

Solve:  

Possible Answers:

Correct answer:

Explanation:

In order to solve this equation, we will need to change the base of one half to two. Use a negative exponent to rewrite this term.

Rewrite the equation.

Since the bases are common, we can simply set the exponents equal to each other.

Solve for x.  Divide a negative one on both sides to eliminate the negatives.

The equation becomes:

Subtract  from both sides.

Divide both sides by negative four.

The answer is:  

Example Question #75 : Solving Exponential Equations

Solve for .

Possible Answers:

Correct answer:

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.

 With the same base, we can now write

 Subtract  on both sides.

Example Question #76 : Solving Exponential Equations

Solve for .

Possible Answers:

Correct answer:

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.

 With the same base, we can now write

 Subtract  on both sides.

Example Question #77 : Solving Exponential Equations

Solve for .

Possible Answers:

Correct answer:

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.

 With the same base, we can now write

 Subtract  on both sides.

Example Question #78 : Solving Exponential Equations

Solve for .

Possible Answers:

Correct answer:

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.

 With the same base, we can now write

 Subtract  on both sides.

 Divide  on both sides.

Example Question #79 : Solving Exponential Equations

Solve for .

Possible Answers:

Correct answer:

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

 therefore

 With the same base, we can now write

 Subtract  on both sides.

 Divide  on both sides.

Example Question #80 : Solving Exponential Equations

Solve for .

Possible Answers:

Correct answer:

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

 therefore

 With the same base, we can now write

 Add  on both sides.

 Divide  on both sides.

Example Question #81 : Solving Exponential Equations

Solve for .

Possible Answers:

Correct answer:

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

 therefore

 With the same base, we can now write

 Add  on both sides.

 Divide  on both sides.

Example Question #82 : Solving Exponential Equations

Solve for .

Possible Answers:

Correct answer:

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

 therefore

 With the same base, we can now write

 Subtract  on both sides.

 Divide  on both sides.

Example Question #81 : Solving And Graphing Exponential Equations

Solve for .

Possible Answers:

Correct answer:

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

 therefore

 Apply power rule of exponents.

 With the same base, we can now write

 Subtract  on both sides.

 Divide  on both sides.

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