Rules of Logarithms

The rules work because logs are powers

Example 1

Express as single logarithm

Log_a(12) + Log_a(4) = Log_a(48)

Example 2

Express as single logarithm

Log_a(50) - Log_a(5) = Log_a(10)

Example 3

Express as single logarithm

Log_a(m) + Log_a(n) = Log_a(mn)

Example 4

Express in terms of Log_na, Log_nb, Log_nc

Log_nabc = Log_na + Log_nb + Log_nc

Example 5

Express in terms of Log_na, Log_nb, Log_nc

Log_na² = 2Log_na