# Algebra II : Solving Exponential Equations

## Example Questions

### Example Question #31 : Solving Exponential Equations

Solve the equation:

Explanation:

In order to determine the value of x, we will need to convert the base of one-tenth to the base of ten.

Rewrite the fraction as a base of ten.

Rewrite the right side of the equation using the new term.

According to the product rule for exponents, we can set the powers equal since the bases are similar.

Divide by negative one on both sides.

Subtract  on both sides.  The equation will become:

Divide by negative two on both sides.

### Example Question #32 : Solving Exponential Equations

Solve:

Explanation:

In order to solve this, we will need to rewrite the right side as the similar base to the left side of the equation.

Rewrite the right side.

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

Subtract  on both sides.

Divide by two on both sides.

### Example Question #33 : Solving Exponential Equations

Solve:

Explanation:

To solve this equation, we will need to convert the 100 into base ten.

Rewrite the number using this base.

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

Simplify this equation.

Subtract  on both sides.

### 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.