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Logarithms Part II
Better set of flashcards on logs
26
Mathematics
Undergraduate 1
08/28/2009

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Cards

Term

How do you re-write

logbA = x in exponent form?

Definition

bx = A

Example 1:

If given log28 = x, you would rewrite it in exponent form as 2x = 8.

 

Example 2:

If given log39 = x, you would rewrite it in exponent form as 3x = 9

 

Example #3:

If given log5125 = x, you would re-write it in exponent form as 5x = 125

Term
What is exponent form?
Definition

bx = A

An equation is in exponent form when you have a base raised to an unknown power.

 

Example 1:              

6x = 36 

Example 2:

3x = 27

Term
What is logarithmic form?
Definition

logbA = x

Logarithmic form is when the exponent is the result.

The word "log" is just an instruction that tells you what to do (solve for the exponent).

Term

Identify each part of the following equation in exponent form:

 

bx = A

 

1) What is the exponent?

2) What is the base?

3) What is the result?

Definition

1) x

2) b

3) A

Term

Identify each part of the logarithm:

 

logbA = x

 

1) What is the base?

2) What is the exponent?

3) What is the "result"?

Definition

1) b

2) x

3) A

Term

How are

logbA = x and bx = A related?

Definition

They are two ways of expressing exponents. Sometimes it is easier to see the answer if you re-write a log into an exponent.

Term

How do you expand

logb(a·c)?

Definition

logba + logbc

 

Rewrite it as the sum of two logarithms. Both logarithms have the same base, but they have different "results".

 

Note: If you had logb(a·c·d), you would write is

logba + logbc + logbd

Term
How do you expand logb(a/c)?
Definition

logba - logbc

 

Rewrite as the difference of two logs. Both logs have the same base, but different "results".

 

 

Term

How do you expand

logbAP?

Definition

P·logbA

logbAP is logbA raised to the power P. To re-write it move P to the front of the log and multiply the log by P.

 

 

Term
How do you re-write lnA so that it looks like a regular logarithm (so it is in the form logbA)?
Definition

logeA

 

In this situation, e is Euler's number, not a variable. So, the base is e.

 

 

Term
Re-write lnA = x in exponent form
Definition

ex = A

 

Ln means a log with base e.

Term
What is euler's number?
Definition

Euler's number is a mathematical constant like pi. It roughly equals 2.71828 18284 59045 23536.

It is represented by the lower

case letter e.

Term
If given log100 = x, what base is implied?
Definition

Base 10 is implied. For example, log100 = x, is log10100 = x

If you are given log2 = x, base ten is still implied. So, log2 = x can be re-written as log102 = x

Term
Do logA and lnA have the same implied base?
Definition

NO!

Both logA and lnA have implied bases, but the implied base of logA is 10 and the implied base of lnA is e.

Term
What is the change of base formula, and what does it do?
Definition

The change of base formula is:

logbA = lnA / lnb

 

The change of base formula lets you re-write a log of any base, b, into a natural log (a log of base e, or ln)

Term

Say you're given log28 = x. What is the value of x?

(Rewrite in exponent form first, then solve for x)

Definition

log28 = x re-written in exponent form:

2x = 8

x = 3

 

 

Term
Say you're given log636 = x. What is the value of x?
Definition

log636 = x re-written as in exponent form:

6x = 36

x = 2

Term
If given log4(3·a), how do you expand it?
Definition
log43 + log4a
Term
If given log9(4·500), how do you expand it?
Definition
log94 + log9500
Term
If given log8(ab), how do you expand it?
Definition
log8a + log8b
Term
If given log7(49/343), how do you re-write it?
Definition
log749 - log7343
Term
If given log3(a/9), how do you re-write it?
Definition
log3a - log39
Term
If given log2(8/a), how do you expand it?
Definition
log28 - log2a
Term
If given log4(a/b), how do you expand it?
Definition
log4a - log4b
Term
If given log392, how do you expand it?
Definition
2log39
Term
If given log216a, how do you expand it?
Definition
alog216
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