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Logarithm Rules and Values

What a logarithm means, the laws of logarithms and common log values.

44 cardsGrades 9–12, College#logarithms#exponentials#algebra

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44 cards
  • Definition of a logarithmRule
    log_b(x) = y means bʸ = x
  • Product ruleRule
    log_b(xy) = log_b x + log_b y
  • Quotient ruleRule
    log_b(x/y) = log_b x − log_b y
  • Power ruleRule
    log_b(xⁿ) = n log_b x
  • Change of baseRule
    log_b x = log x / log b (any base)
  • Log of 1Rule
    log_b 1 = 0
  • Log of the baseRule
    log_b b = 1
  • Inverse property 1Rule
    b^(log_b x) = x
  • Inverse property 2Rule
    log_b(bˣ) = x
  • Common logarithmRule
    Base 10, written log x
  • Natural logarithmRule
    Base e, written ln x
  • Binary logarithmRule
    Base 2, written log₂ x
  • Domain of log xRule
    x > 0
  • log of a negative numberRule
    Not defined among the real numbers
  • log 100Rule
    2
  • log 1,000Rule
    3
  • log 0.1Rule
    −1
  • log 0.01Rule
    −2
  • log 10Rule
    1
  • log₂ 8Rule
    3
  • log₂ 64Rule
    6
  • log₂ 1024Rule
    10
  • log₃ 81Rule
    4
  • log₅ 125Rule
    3
  • log₄ 2Rule
    1/2
  • log₂ (1/8)Rule
    −3
  • ln eRule
    1
  • ln 1Rule
    0
  • ln(e²)Rule
    2
  • e^(ln 5)Rule
    5
  • Expand log(ab/c)Rule
    log a + log b − log c
  • Condense 2 log x + log yRule
    log(x²y)
  • Solve 2ˣ = 16Rule
    x = 4
  • Solve 3ˣ = 5Rule
    x = log 5 / log 3 (about 1.465)
  • Solve log₂ x = 5Rule
    x = 32
  • Is log(x + y) = log x + log y?Rule
    No. The product rule needs log(xy)
  • Is log(x)/log(y) the same as log(x/y)?Rule
    No. They are different quantities
  • Graph of y = log x: vertical asymptoteRule
    x = 0
  • Graph of y = log x: x-interceptRule
    x = 1
  • Value of e (to 5 decimals)Rule
    2.71828
  • Half-life formula ideaRule
    Amount = start × (1/2)^(t / half-life)
  • Decibel scale usesRule
    A logarithm of a power ratio (10 log₁₀)
  • Richter scale usesRule
    A base-10 logarithm of shaking amplitude
  • pH formulaRule
    pH = −log₁₀[H⁺]

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