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

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

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Expansion of Numbers and Operations

+addition (−subtraction) ↺ ·multiplication (/division) ↺ ˄exponentiation (˅root ⍻logarithm)

5216#4882 SIBLINGS CHILDREN 4882

+addition (−subtraction) ↺ ·multiplication (/division) ↺ ˄exponentiation (˅root ⍻logarithm)

5216#4882 SIBLINGS CHILDREN 4882

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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)

5216#5283 SIBLINGS CHILDREN 5283

① (p˄m)·(p˄n) = p˄(m+n) ② (p˄m)˄n = p˄(m·n) ③ (p·q)˄n = (p˄n)·(q˄n)

5216#5283 SIBLINGS CHILDREN 5283

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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

5216#9666 SIBLINGS CHILDREN 9666

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 SIBLINGS CHILDREN 9666

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05 Exponents In Algebra

Algebra Basics: Exponents In Algebra - Math Antics

5216#3799 SIBLINGS CHILDREN 3799

Algebra Basics: Exponents In Algebra - Math Antics

5216#3799 SIBLINGS CHILDREN 3799

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08 Simplifying Expressions With Roots and Exponents

Simplifying Expressions With Roots and Exponents

5216#3801 SIBLINGS CHILDREN 3801

Simplifying Expressions With Roots and Exponents

5216#3801 SIBLINGS CHILDREN 3801

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09 Solving Algebraic Equations With Roots and Exponents

Solving Algebraic Equations With Roots and Exponents

5216#3802 SIBLINGS CHILDREN 3802

Solving Algebraic Equations With Roots and Exponents

5216#3802 SIBLINGS CHILDREN 3802

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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.

5216#3638 SIBLINGS CHILDREN 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.

5216#3638 SIBLINGS CHILDREN 3638

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42 Logarithms Part 2

Base Ten Logs, Natural Logs, and the Change-Of-Base Property

5216#3639 SIBLINGS CHILDREN 3639

Base Ten Logs, Natural Logs, and the Change-Of-Base Property

5216#3639 SIBLINGS CHILDREN 3639

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43 Logarithms Part 3

Logarithms Part 3: Properties of Logs, Expanding Logarithmic Expressions

5216#3640 SIBLINGS CHILDREN 3640

Logarithms Part 3: Properties of Logs, Expanding Logarithmic Expressions

5216#3640 SIBLINGS CHILDREN 3640

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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.

5216#3798 SIBLINGS CHILDREN 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.

5216#3798 SIBLINGS CHILDREN 3798

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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.

5216#3625 SIBLINGS CHILDREN 3625

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

5216#3625 SIBLINGS CHILDREN 3625

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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"

5216#9671 SIBLINGS CHILDREN 9671

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 SIBLINGS CHILDREN 9671

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Logarithm

"the log, base b, of x" "To what power must b be raised, in order to yield x?"

5216#9638 SIBLINGS CHILDREN 9638

"the log, base b, of x" "To what power must b be raised, in order to yield x?"

5216#9638 SIBLINGS CHILDREN 9638

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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.

5216#3738 SIBLINGS CHILDREN 3738

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

5216#3738 SIBLINGS CHILDREN 3738

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Logarithms Explained

What is the power that I should raise this base to in order to get this number?

5216#9635 SIBLINGS CHILDREN 9635

What is the power that I should raise this base to in order to get this number?

5216#9635 SIBLINGS CHILDREN 9635

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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?"

5216#9637 SIBLINGS CHILDREN 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?"

5216#9637 SIBLINGS CHILDREN 9637