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Properties and Applications of Logarithms in Precalculus

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Terms in this set (18)

  • Product Rule of Logarithms

    log_b(xy) = log_b x + log_b y. The logarithm of a product equals the sum of the logarithms.

  • Quotient Rule of Logarithms

    log_b(x/y) = log_b x - log_b y. The logarithm of a quotient equals the difference of the logarithms.

  • Power Rule of Logarithms

    log_b(x^r) = r log_b x. The logarithm of a power equals the exponent times the logarithm of the base.

  • Change of Base Formula

    log_b a = (log_c a) / (log_c b). Used to evaluate logarithms with any base using a calculator.

  • Expanding log_b(9x)

    log_b 9 + log_b x

  • Expanding log_b(1000x)

    log_b 1000 + log_b x = 3 + log_b x

  • Expanding log_5(125/y)

    log_5 125 - log_5 y = 3 - log_5 y

  • Expanding log_b(xy^3)

    log_b x + 3 log_b y

  • Condensing log_b x + log_b y

    log_b (xy)

  • Condensing log_b x - log_b y

    log_b (x/y)

  • Condensing r log_b x

    log_b (x^r)

  • Expanding ln(a^8 / b^3)

    8 ln a - 3 ln b

  • Expanding log_6(x^3 (x - 6)^5)

    3 log_6 x + 5 log_6 (x - 6)

  • Expanding ln(((x + 1)^4) / (x^2 - 3))

    4 ln (x + 1) - ln (x^2 - 3)

  • Expanding log((x(x + 8)) / 4)

    log x + log (x + 8) - log 4

  • Evaluating log_5 9

    Approximately 1.3652

  • Evaluating log_24 308

    Approximately 1.8030

  • Evaluating log_14 36.9

    Approximately 1.3672