Exponential Functions - College Algebra

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.

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.

The answer is:

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!

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!

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

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,

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:

, 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 :

,

So,

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.

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.

The answer is:

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!

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!

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

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,

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:

, 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 :

,

So,

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.