# Algebra II : Solving and Graphing Exponential Equations

## Example Questions

### Example Question #41 : Solving Exponential Equations

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.

### Example Question #42 : Solving Exponential Equations

Solve:

Explanation:

Convert all the terms to base ten.

Use distribution to simplify the powers in parentheses.

On the left side, since we are multiplying powers of the same base, we can add the exponents.

Set the powers equal to each other now that the bases are similar.

Subtract  on both sides.

Divide by negative 19 on both sides.

### Example Question #43 : Solving Exponential Equations

Solve:

Explanation:

Convert the base of the right side to base four.

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

Simplify the right side.

Subtract  on both sides.

Divide by negative six on both sides.

Reduce both fractions.

### Example Question #44 : Solving Exponential Equations

Solve:

Explanation:

In order to solve this equation, we will need to change the bases of both terms.

Notice that both bases can be four raised to some power.

Replace the terms.

Set the powers equal to each other.

Divide by two on both sides.

Subtract  on both sides.

Divide by seven on both sides.

### Example Question #45 : Solving Exponential Equations

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.

### Example Question #46 : Solving Exponential Equations

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.

### Example Question #47 : Solving Exponential Equations

Solve:

Explanation:

Rewrite the second term in terms of base two.

Rewrite the equation.

Set the powers equal to each other.

Do NOT divide by x on both sides or we will get no solution!

Instead, subtract  from both sides.

The equation becomes:

Divide by 255 on both sides.

### Example Question #51 : Solving Exponential Equations

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:

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

### Example Question #52 : Solving Exponential Equations

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. 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.

Solve for .