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"

9550

○ "square root of x" -> x ∨ 2, "x root 2" ○ "log base b of x" -> x ∀ b, "x log b"

9550

•
08 Simplifying Expressions With Roots and Exponents

Simplifying Expressions With Roots and Exponents

3801

Simplifying Expressions With Roots and Exponents

3801

•
09 Solving Algebraic Equations With Roots and Exponents

Solving Algebraic Equations With Roots and Exponents

3802

Solving Algebraic Equations With Roots and Exponents

3802

•
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

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

•
43 Logarithms Part 3

Logarithms Part 3: Properties of Logs, Expanding Logarithmic Expressions

3640

Logarithms Part 3: Properties of Logs, Expanding Logarithmic Expressions

3640

•
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

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

You can expect the difference between one x value at any point to be the same as any other.

3625

•
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.

9603 COMMENT

○ 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.

9603 COMMENT

•
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.

9628

○ (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.

9628

•
Logarithms Explained

In the same way that division is the inverse of multiplication a logarithm is just the inverse of exponentiation.

3738

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

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

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

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