trustle > EngliSea > Corona Safe Schooling > mathematics > Quick Math Index > 31 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
○ "square root of x" -> x ∨ 2, "x root 2" ○ "log base b of x" -> x ∀ b, "x log b"
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05 Exponents In Algebra
Algebra Basics: Exponents In Algebra - Math Antics
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07 Square Roots, Cube Roots, and Other Roots
Square Roots, Cube Roots, and Other Roots
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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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14 Understanding Exponents and Their Operations
Understanding Exponents and Their Operations
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40 Evaluating and Graphing Exponential Functions
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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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44 Solving Exponential and Logarithmic Equations
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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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Logarithm
"the log, base b, of x" "To what power must b be raised, in order to yield x?"
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Logarithm Properties
○ 1 ∀ b = 0, The power that the base must be raised to in order to yield 1 is the 0th. ○ b ∀ b = 1, The power that the base must be raised to in order to yield the base itself is the 1st.
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Logarithm Properties
○ (b∧x) ∀ b = x, The power that the base must be raised to in order to yield the base raised to the power of a number is the power of the number. ○ b ∧ (b∀x) = x, A number raised to the power that the number must be raised to in order to yield x is 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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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?"
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Triangle of Power
Triangle of Power
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