# 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.

**(13.4)**

**(13.5)**

**(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 $8\hspace{0.17em}\times \hspace{0.17em}16\hspace{0.17em}=\hspace{0.17em}128.$ Writing these numbers as powers of 2, we have

Get *Basic Technical Mathematics, 11th Edition* now with the O’Reilly learning platform.

O’Reilly members experience live online training, plus books, videos, and digital content from nearly 200 publishers.