Exponential and Logarithm Laws

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Flashcards

Exponential Law: Product of Powers

When multiplying exponential terms with the same base, add the exponents: a^(m+n)

Exponential Law: Quotient of Powers

When dividing exponential terms with the same base, subtract the exponents: a^(m-n)

Exponential Law: Power of a Power

When raising a power to another power, multiply the exponents: a^(mn)

Exponential Law: Power of a Product

The power of a product is the product of the powers: a^m * b^m

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Exponential Law: Power of a Quotient

The power of a quotient is the quotient of the powers: a^m / b^m

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Exponential Law: Zero Exponent

Any non-zero number raised to the power of 0 is 1.

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Exponential Law: Fractional Exponent

Relates fractional exponents to radicals

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Exponential Law: Negative Exponent

A negative exponent indicates the reciprocal of the base raised to the positive exponent

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Logarithm Law: Product Rule

The logarithm of a product is the sum of the logarithms: log(a) + log(b)

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Logarithm Law: Quotient Rule

The logarithm of a quotient is the difference of the logarithms: log(a) - log(b)

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Logarithm Law: Power Rule

The logarithm of a number raised to a power is the product of the power and the logarithm of the number: n*log(b)

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Logarithm Law: log_a(a)

The logarithm of the base to itself is always 1.

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Logarithm Law: log_a(1)

The logarithm of 1 to any base is always 0.

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Logarithm Law: Change of Base

Used to change the base of a logarithm to another base for simplification or calculation

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Study Notes

Exponential Laws

  • General form: M = bn
  • Rule 1: am × an = am+n
  • Rule 2: am ÷ an = am-n
  • Rule 3: (am)n = amn
  • Rule 4: (ab)m = am × bm
  • Rule 5: (a/b)m = am / bm
  • Rule 6: a0 = 1
  • Rule 7: a1/n = n√a
  • Rule 8: a-m = 1 / am

Logarithm Laws

  • General form: logbM = n
  • Rule 1: logm(a × b) = logma + logmb
  • Rule 2: logm(a/b) = logma - logmb
  • Rule 3: logm(bn) = n logmb
  • Rule 4: logaa = 1
  • Rule 5: loga1 = 0
  • Rule 6: blogbr = r
  • Rule 7: logmb = lognb / lognm

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