Precalculus A Fuctional Approach to Graphing and Problem Solving

Section 4.6: Logarithmic Equations
Essential Ideas

  • Log of Both Sides Theorem
    If A, B, and b are positive real numbers with b not equal to 1, then
                                      logbA = logbB
    is equivalent to A = b.

  • Logarithmic Equations
    Log Type I:   The unknown is the logarithm.
    Log Type II: The unknown is the base.
    Log Type III: The logarithm of an unknown is equal to a number.
    Log Type IV: The logarithm of an unknown is equal to the logarithm of a number.

  • Laws of Logarithms
    Let A, B, and b be positive numbers (b not equal to 1) and let p be any real number,
          First law (Additive):             logb(AB) = logbA + logbB
          Second law (Subtractive):    logb(A/B) = logbA + logbB
          Third law (Multiplicative):      logb(A)p = P  logbA

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© 2011 Karl J. Smith. All rights reserved.