# Connexions

You are here: Home » Content » Advanced Algebra II: Conceptual Explanations » Common Logarithms

• How to Use Advanced Algebra II

### Lenses

What is a lens?

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

#### Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
• Bookshare

This collection is included inLens: Bookshare's Lens
By: Bookshare - A Benetech Initiative

"DAISY and BRF versions of this collection are available."

Click the "Bookshare" link to see all content affiliated with them.

• Featured Content

This collection is included inLens: Connexions Featured Content
By: Connexions

"This is the "concepts" book in Kenny Felder's "Advanced Algebra II" series. This text was created with a focus on 'doing' and 'understanding' algebra concepts rather than simply hearing about […]"

Click the "Featured Content" link to see all content affiliated with them.

Click the tag icon to display tags associated with this content.

#### Also in these lenses

• Busbee's Math Materials

This collection is included inLens: Busbee's Math Materials Lens
By: Kenneth Leroy Busbee

Click the "Busbee's Math Materials" link to see all content selected in this lens.

Click the tag icon to display tags associated with this content.

### Recently Viewed

This feature requires Javascript to be enabled.

### Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Inside Collection (Textbook):

Textbook by: Kenny M. Felder. E-mail the author

# Common Logarithms

Module by: Kenny M. Felder. E-mail the author

Summary: This module covers some of the logarithms commonly encountered in algebra.

When you see a root without a number in it, it is assumed to be a square root. That is, 2525 size 12{ sqrt {"25"} } {}is a shorthand way of writing 252252 size 12{ nroot { size 8{2} } {"25"} } {}. This rule is employed because square roots are more common than other types.

When you see a logarithm without a number in it, it is assumed to be a base 10 logarithm. That is, log(1000)log(1000) size 12{"log" $$"1000"$$ } {} is a shorthand way of writing log10(1000)log10(1000) size 12{"log" rSub { size 8{"10"} } $$"1000"$$ } {}. A base 10 logarithm is also known as a “common” log.

Why are common logs particularly useful? Well, what is log10(1000)log10(1000) size 12{"log" rSub { size 8{"10"} } $$"1000"$$ } {}? By now you know that this asks the question “10 to what power is 1000?” The answer is 3. Similarly, you can confirm that:

log ( 10 ) = 1 log ( 10 ) = 1 size 12{"log" $$"10"$$ =1} {}
(1)
log ( 100 ) = 2 log ( 100 ) = 2 size 12{"log" $$"100"$$ =2} {}
(2)
log ( 1, 000 , 000 ) = 6 log ( 1, 000 , 000 ) = 6 size 12{"log" $$1,"000","000"$$ =6} {}
(3)

We can also follow this pattern backward:

log ( 1 ) = 0 log ( 1 ) = 0 size 12{"log" $$1$$ =0} {}
(4)
log 1 10 = 1 log 1 10 = 1 size 12{"log" left ( { {1} over {"10"} } right )= - 1} {}
(5)
log 1 100 = 2 log 1 100 = 2 size 12{"log" left ( { {1} over {"100"} } right )= - 2} {}
(6)

and so on. In other words, the common log tells you the order of magnitude of a number: how many zeros it has. Of course, log10(500)log10(500) size 12{"log" rSub { size 8{"10"} } $$"500"$$ } {} is difficult to determine exactly without a calculator, but we can say immediately that it must be somewhere between 2 and 3, since 500 is between 100 and 1000.

## Content actions

PDF | EPUB (?)

### What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

PDF | EPUB (?)

### What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

#### Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

#### Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks