Solving Exponential Equations

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Algebra II › Solving Exponential Equations

Questions 1 - 10
1

Solve for .

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.

2

Solve for .

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 now write

Add and subtract on both sides.

3

Solve for .

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 same base, we can write:

Subtract on both sides.

Divide on both sides.

4

Solve for .

Explanation

When we add exponents, we try to factor to see if we can simplify it. Let's factor . We get . Remember to apply the rule of multiplying exponents which is to add the exponents and keeping the base the same.

With the same base, we can rewrite as .

5

Solve for .

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 now write

Take the square root on both sides. Account for negative answer.

6

Solve for .

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:

Add on both sides.

Divide on both sides.

7

Solve for .

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.

8

Solve for :

No solution

Explanation

Because both sides of the equation have the same base, set the terms equal to each other.

Add 9 to both sides:

Then, subtract 2x from both sides:

Finally, divide both sides by 3:

9

Solve for .

Explanation

When we add exponents, we try to factor to see if we can simplify it. Let's factor . We get . Remember to apply the rule of multiplying exponents which is to add the exponents and keeping the base the same.

With the same base, we can rewrite as .

10

Solve:

Explanation

Rewrite the right side with a negative exponent. The goal is to establish similar bases to set the powers equal to each other.

Set the powers equal to each other.

Subtract one from both sides.

Divide by three sides.

The answer is:

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