• +addition┆−subtraction
➊ Natural numbers are closed under addition. ➋ Subtraction is the inverse operation of addition. p + q = r r - q = p r - p = q If p or q is greater than r, the result is not a natural number. By defining integers to contain 0 and negative numbers, they b ...
5216#17366 SBLNGS CHLDRN 17366

○○○ +addition┆−subtraction ⪢⪢
5216#39181 SBLNGS CHLDRN 39181

• +addition┆−subtraction
5216#39184 SBLNGS CHLDRN 39184

• ·multiplication┆/division
➌ Multiplication is repeated addition. p + p + p = p·3 p·0 means 'adding p zero times', which is 0. If we define p·(-q) as 'subtracting p q times', then integers are closed under multiplication too. ➍ Division is the inverse operation of multiplication. ...
5216#4882 SBLNGS CHLDRN 4882

• ·multiplication┆/division
5216#39178 SBLNGS CHLDRN 39178

• ·multiplication┆/division
5216#39185 SBLNGS CHLDRN 39185

• ˄exponentiation┆˅root
➎ Exponentiation is repeated multiplication. p · p · p = p ˄ 3 p ˄ 1 means 'multiplying p one time', which means 'adding p one time', that is p. (p˄m)·(p˄n) = p˄(m+n) (p˄m)˄n = p˄(m·n) (p·q)˄n = (p˄n)·(q˄n) ➏ Root is the inverse operation of exponentiati ...
5216#39179 SBLNGS CHLDRN 39179

• ˄exponentiation┆˅root
5216#39182 SBLNGS CHLDRN 39182

• ˄exponentiation┆˅root
5216#39186 SBLNGS CHLDRN 39186

• ˄exponentiation┆⍻logarithm
➐ Logarithm is another inverse operation of exponentiation. p ˄ q = r r ⍻ p = q
5216#39180 SBLNGS CHLDRN 39180

• ˄exponentiation┆⍻logarithm
5216#39183 SBLNGS CHLDRN 39183

• ˄exponentiation┆⍻logarithm
5216#39187 SBLNGS CHLDRN 39187

• Logarithm Properties
① 1⍻b = 0 ② b⍻b = 1 ③ (b˄x)⍻b = x ④ b˄(x⍻b) = x ⑤ (x˄p)⍻b = p·(x⍻b) ⑥ x⍻b = (x⍻c)/(b⍻c) ⑦ (x·y)⍻b = x⍻b+y⍻b ⑧ (x/y)⍻b = x⍻b-y⍻b
5216#9666 SBLNGS CHLDRN 9666

• 05 Exponents In Algebra
Algebra Basics: Exponents In Algebra - Math Antics
5216#3799 SBLNGS CHLDRN 3799

• 07 Square Roots, Cube Roots, and Other Roots
5216#3800 SBLNGS CHLDRN 3800

• 08 Simplifying Expressions With Roots and Exponents
Simplifying Expressions With Roots and Exponents
5216#3801 SBLNGS CHLDRN 3801

• 09 Solving Algebraic Equations With Roots and Exponents
Solving Algebraic Equations With Roots and Exponents
5216#3802 SBLNGS CHLDRN 3802

Pillow English Listening

• 14 Understanding Exponents and Their Operations
5216#3804 SBLNGS CHLDRN 3804

• 40 Evaluating and Graphing Exponential Functions
5216#3803 SBLNGS CHLDRN 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.
5216#3638 SBLNGS CHLDRN 3638

• 42 Logarithms Part 2
Base Ten Logs, Natural Logs, and the Change-Of-Base Property
5216#3639 SBLNGS CHLDRN 3639

• 43 Logarithms Part 3
Logarithms Part 3: Properties of Logs, Expanding Logarithmic Expressions
5216#3640 SBLNGS CHLDRN 3640

• 44 Solving Exponential and Logarithmic Equations
5216#3464 SBLNGS CHLDRN 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.
5216#3798 SBLNGS CHLDRN 3798

• exponential function
You can expect the difference between one x value at any point to be the same as any other.
5216#3625 SBLNGS CHLDRN 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"
5216#9671 SBLNGS CHLDRN 9671

◌◌◌ Interest
Simple And Compound Interest And Spreadsheet Intro
5216#9774 SBLNGS CHLDRN 9774

◌◌◌ Logarithm
"the log, base b, of x" "To what power must b be raised, in order to yield x?"
5216#9638 SBLNGS CHLDRN 9638

• Logarithm Equations
5216#9772 SBLNGS CHLDRN 9772

• Logarithms Explained
In the same way that division is the inverse of multiplication a logarithm is just the inverse of exponentiation.
5216#3738 SBLNGS CHLDRN 3738

• Logarithms Explained
What is the power that I should raise this base to in order to get this number?
5216#9635 SBLNGS CHLDRN 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?"
5216#9637 SBLNGS CHLDRN 9637

• x⍻b
ᐥWhat power do you have to raise b to in order to get x?ᐥ
5216#17402 SBLNGS CHLDRN 17402