trustle > EngliSea > Corona Safe Schooling > mathematics > Quick Math Index > 25 Exponent, root and logarithm

Exponentiation is repeated multiplication. Root is the inverse operation of exponentiation. Logarithm is a new inverse operation of exponentiation.
 
Expansion of Numbers and Operations
9550
 
Expansion of Numbers and Operations
➊ Addition
The whole numbers are closed under addition.

➋ Subtraction is the inverse operation of addition.
l + m = n
n - m = l
Define negative integers then integers are closed under subtraction.

➌ Multiplication is repeated addition.
p + p + p = p·3
p ...
4882
 
Logarithm Properties
➊ 1⍻b = 0
The power that the base must be raised to in order to yield 1 is the 0th.

➋ b⍻b = 1
The power that the base must be raised to in order to yield the base itself is the 1st.

➌ (b˄x)⍻b = x
The power that the base must be raised to in order to yie ...
9666
 
05 Exponents In Algebra
Algebra Basics: Exponents In Algebra - Math Antics
3799
 
07 Square Roots, Cube Roots, and Other Roots
3800
 
08 Simplifying Expressions With Roots and Exponents
Simplifying Expressions With Roots and Exponents
3801
 
09 Solving Algebraic Equations With Roots and Exponents
Solving Algebraic Equations With Roots and Exponents
3802
 
14 Understanding Exponents and Their Operations
3804
 
40 Evaluating and Graphing Exponential Functions
3803
 
41 Logarithms Part 1
When we say log base b of x equals y, we are saying b to the y equals x. With logs, the base of the log raised to the power of what's on the other side of the equal sign will equal the number that the log is operating on.
3638
 
42 Logarithms Part 2
Base Ten Logs, Natural Logs, and the Change-Of-Base Property
3639
 
43 Logarithms Part 3
Logarithms Part 3: Properties of Logs, Expanding Logarithmic Expressions
3640
 
44 Solving Exponential and Logarithmic Equations
3464
 
Change of base
Log base b of n. What power should I put in the exponent of b so b to that power will give me n.
3798
 
exponential function
You can expect the difference between one x value at any point to be the same as any other.
3625
 
Exponentiation
b˄n is called "b raised to the n-th power", "b raised to the power of n", "the n-th power of b", "b to the n-th", or most briefly as "b to the n"
9671
 
Interest
Simple And Compound Interest And Spreadsheet Intro
9774
 
Introduction To Exponential Functions
5283
 
Logarithm
"the log, base b, of x" "To what power must b be raised, in order to yield x?"
9638
 
Logarithm Equations
9772
 
Logarithms Explained ▷▷▷
In the same way that division is the inverse of multiplication a logarithm is just the inverse of exponentiation.
3738
 
Logarithms Explained
What is the power that I should raise this base to in order to get this number?
9635
 
Logarithms Explained
Anytime you see log base b of some number n, you can think about it as asking the question "What power do I need to put in my exponent to get b to that power equal to this number n?"
9637
 
Saying Logarithm
By definition, when we say log base b of x equals y, that's the same thing as saying "b to the y equals x". So if you want to find log base b of x, you're asking "what power do you have to raise b to in oder to get x?"
3795

-