Term
How do you rewrite
log_{b}A = x in exponent form? 

Definition
b^{x }= A^{}
Example 1:
If given log_{2}8 = x, you would rewrite it in exponent form as 2^{x }= 8.
Example 2:
If given log_{3}9 = x, you would rewrite it in exponent form as 3^{x} = 9
Example #3:
If given log_{5}125 = x, you would rewrite it in exponent form as 5^{x} = 125 


Term

Definition
b^{x} = A
An equation is in exponent form when you have a base raised to an unknown power.
Example 1:
6^{x }= 36
Example 2:
3^{x} = 27 


Term
What is logarithmic form? 

Definition
log_{b}A = 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:
b^{x }= A
1) What is the exponent?
2) What is the base?
3) What is the result? 

Definition


Term
Identify each part of the logarithm:
log_{b}A = x
1) What is the base?
2) What is the exponent?
3) What is the "result"? 

Definition


Term
How are
log_{b}A = x and b^{x} = A related? 

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


Term
How do you expand
log_{b}(a·c)? 

Definition
log_{b}a + log_{b}c
Rewrite it as the sum of two logarithms. Both logarithms have the same base, but they have different "results".
Note: If you had log_{b}(a·c·d), you would write is
log_{b}a + log_{b}c + log_{b}d 


Term
How do you expand log_{b}(a/c)? 

Definition
log_{b}a  log_{b}c
Rewrite as the difference of two logs. Both logs have the same base, but different "results".



Term
How do you expand
log_{b}A^{P}? 

Definition
P·log_{b}A
log_{b}A^{P }is log_{b}A raised to the power P. To rewrite it move P to the front of the log and multiply the log by P.



Term
How do you rewrite lnA so that it looks like a regular logarithm (so it is in the form log_{b}A)? 

Definition
log_{e}A
In this situation, e is Euler's number, not a variable. So, the base is e.



Term
Rewrite lnA = x in exponent form 

Definition
e^{x} = A
Ln means a log with base e.



Term

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 log_{10}100 = x
If you are given log2 = x, base ten is still implied. So, log2 = x can be rewritten as log_{10}2 = 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:
log_{b}A = lnA / lnb
The change of base formula lets you rewrite a log of any base, b, into a natural log (a log of base e, or ln) 


Term
Say you're given log_{2}8 = x. What is the value of x?
(Rewrite in exponent form first, then solve for x) 

Definition
log_{2}8 = x rewritten in exponent form:
2^{x} = 8
x = 3



Term
Say you're given log_{6}36 = x. What is the value of x? 

Definition
log_{6}36 = x rewritten as in exponent form:
6^{x} = 36
x = 2 


Term
If given log_{4}(3·a), how do you expand it? 

Definition


Term
If given log_{9}(4·500), how do you expand it? 

Definition


Term
If given log_{8}(ab), how do you expand it? 

Definition


Term
If given log_{7}(49/343), how do you rewrite it? 

Definition


Term
If given log_{3}(a/9), how do you rewrite it? 

Definition


Term
If given log_{2}(8/a), how do you expand it? 

Definition


Term
If given log_{4}(a/b), how do you expand it? 

Definition


Term
If given log_{3}9^{2}, how do you expand it? 

Definition


Term
If given log_{2}16^{a}, how do you expand it? 

Definition

