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Exponentiation is repeated multiplication.
Root is the inverse operation of exponentiation.
Logarithm is a new inverse operation of exponentiation.

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 ...

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 ...

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 ...

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 ...

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08 Simplifying Expressions With Roots and Exponents

Simplifying Expressions With Roots and Exponents

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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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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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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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43 Logarithms Part 3

Logarithms Part 3: Properties of Logs, Expanding Logarithmic Expressions

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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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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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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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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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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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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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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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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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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