EngliSea > M > math > 25 Exponent, root and logarithm

+plus (−minus) ↺ ·times (/over) ↺ ˄to (˅root ⍻log)

Expansion of Numbers and Operations
+addition (−subtraction) ↺ ·multiplication (/division) ↺ ˄exponentiation (˅root ⍻logarithm)
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Exponentiation Properties
① (p˄m)·(p˄n) = p˄(m+n) ② (p˄m)˄n = p˄(m·n) ③ (p·q)˄n = (p˄n)·(q˄n)
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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
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05 Exponents In Algebra
Algebra Basics: Exponents In Algebra - Math Antics
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08 Simplifying Expressions With Roots and Exponents
Simplifying Expressions With Roots and Exponents
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09 Solving Algebraic Equations With Roots and Exponents
Solving Algebraic Equations With Roots and Exponents
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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.
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42 Logarithms Part 2
Base Ten Logs, Natural Logs, and the Change-Of-Base Property
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43 Logarithms Part 3
Logarithms Part 3: Properties of Logs, Expanding Logarithmic Expressions
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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.
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exponential function
You can expect the difference between one x value at any point to be the same as any other.
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◌◌◌ 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"
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◌◌◌ Interest
Simple And Compound Interest And Spreadsheet Intro
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◌◌◌ Logarithm
"the log, base b, of x" "To what power must b be raised, in order to yield x?"
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Logarithms Explained
In the same way that division is the inverse of multiplication a logarithm is just the inverse of exponentiation.
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Logarithms Explained
What is the power that I should raise this base to in order to get this number?
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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?"
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x⍻b
ᐥWhat power do you have to raise b to in order to get x?ᐥ
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