# College Algebra : Exponential Functions

## Example Questions

### Example Question #1 : Exponential Functions

Solve:

Explanation:

To solve , it is necessary to know the property of .

Since  and the  terms cancel due to inverse operations, the answer is what's left of the  term.

### Example Question #2 : Exponential Functions

Which equation is equivalent to:

Explanation:

So,

### Example Question #3 : Exponential Functions

What is the inverse of the log function?

Explanation:

This is a general formula that you should memorize. The inverse of  is . You can use this formula to change an equation from a log function to an exponential function.

### Example Question #3 : Exponential Functions

Rewrite the following expression as an exponential expression:

Explanation:

Rewrite the following expression as an exponential expression:

Recall the following property of logs and exponents:

Can be rewritten in the following form:

So, taking the log we are given;

We can rewrite it in the form:

So b must be a really huge number!

### Example Question #56 : Understanding Logarithms

Convert the following logarithmic equation to an exponential equation:

Explanation:

Convert the following logarithmic equation to an exponential equation:

Recall the following:

This

Can be rewritten as

So, our given logarithm

Can be rewritten as

Fortunately we don't need to expand, because this woud be a very large number!

### Example Question #4 : Exponential Functions

Convert the following logarithmic equation to an exponential equation.

Explanation:

Convert the following logarithmic equation to an exponential equation.

To convert from logarithms to exponents, recall the following property:

Can be rewritten as:

So, starting with

,

We can get

### Example Question #6 : Exponential Functions

Solve the following:

Explanation:

To solve the following, you must "undo" the 5 with taking log based 5 of both sides. Thus,

The right hand side can be simplified further, as 125 is a power of 5. Thus,

### Example Question #5 : Exponential Functions

Solve for :

(Nearest hundredth)

The equation has no solution.

Explanation:

Apply the Product of Powers Property to rewrite the second expression:

Distribute out:

Divide both sides by 5:

Take the natural logarithm of both sides (and note that you can use common logarithms as well):

Apply a property of logarithms:

Divide by  and evaluate:

### Example Question #6 : Exponential Functions

Solve for :

(Nearest hundredth, if applicable).

The equation has no solution.

Explanation:

, so rewrite the expression at right as a power of 3 using the Power of a Power Property:

Set the exponents equal to each other and solve the resulting linear equation:

Distribute:

Subtract  and 1 from both sides; we can do this simultaneously:

Divide by :