# Algebra II : Solving and Graphing Exponential Equations

## Example Questions

### Example Question #41 : Solving And Graphing Exponential Equations

Solve the equation:

Explanation:

To be able to set the powers equal to each other, we will need common bases.

Convert eight into two cubed.

Set the powers equal to each other.

Divide by three on both sides.

Subtract  from both sides.

Divide by five on both sides.

### Example Question #42 : Solving And Graphing Exponential Equations

Explanation:

To solve this equation, I would first rewrite 8 as a base of 2:

Now, plug back into the equation and simplify. When there are two exponents next to each other like this, multiply them:

Since the bases are the same, you can set the exponents equal to each other:

### Example Question #43 : Solving And Graphing Exponential Equations

Solve:

Explanation:

In order to solve this, the bases of the powers will need to be converted.  Notice that both terms can be rewritten as base three.

Rewrite the equation.

Now that the bases are equal to each other, the powers can be set equal to each other.

Divide negative one on both sides.  This will move the negative to the other side.

Subtract  on both sides.

Divide by negative 18 on both sides.

### Example Question #44 : Solving And Graphing Exponential Equations

Solve the equation:

Explanation:

In order to solve this equation, we will need to change the base on the right side of the equation.

Rewrite the equation.

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

Divide by 200 on both sides.

Simplify both sides.

### Example Question #45 : Solving And Graphing Exponential Equations

Solve the equation:

Explanation:

In order to solve this equation, we will need similar bases to continue.  Notice that both bases have a common base of two.  We can rewrite each base using two to the power of a certain number to express the base.

Rewrite the equation.

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

Divide by 28 on both sides.

### Example Question #46 : Solving And Graphing Exponential Equations

Evaluate:

Explanation:

In order to solve this equation, we will need to convert the bases to a common base.

The one-fifth and 125 can be rewritten as certain powers of five.  Rewrite the numbers.

Replace the numbers with common bases.

Now that the bases are common, we can set the powers equal to each other.

Divide by negative one on both sides.  The equation becomes:

Divide by three on both sides.

### Example Question #47 : Solving And Graphing Exponential Equations

Solve:

Explanation:

The bases of  are already equal.  There is no need to rewrite the right side of the equation using a fraction.

Since the bases are equal, we can set the powers equal to each other.

Subtract three on both sides.

Divide by four on both sides.

### Example Question #48 : Solving And Graphing Exponential Equations

Solve the equation:

Explanation:

Notice that we can rewrite the right side of the equation as an exponent.

The equation  becomes:

Now that the bases of the exponential term are equal, the powers can be set equal to each other.

Simplify the equation.

Divide by six on both sides.

### Example Question #49 : Solving And Graphing Exponential Equations

Solve:

Explanation:

Change the base on the right side to base ten.

Replace the hundred with this term.

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

Solve for the x-variable.  Distribute the two on the right side.

Divide by eight on both sides.

Solve: