13.3 Properties of Logarithms

  • Sum of Logarithms for Product • Difference of Logarithms for Quotient • Multiple of Logarithm for Power • Logarithms of 1 and b

Because a logarithm is an exponent, it must follow the laws of exponents. The laws used in this section to derive the very useful properties of logarithms are listed here for reference.

bubv = bu + v (13.4)
bubv = bu − v (13.5)
(bu)n = bnu (13.6)

The next example shows the reasoning used in deriving the properties of logarithms.

EXAMPLE 1 Sum of logarithms for product

We know that 8 × 16 = 128. Writing these numbers as powers of 2, we have

8 = 2316 = 24128 = 2

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