What are some of the basic log rules?

By: Suresh Kumar Mukhiya - In: Linear Algebra - 0 comments

) log_b(mn) = log_b(m) + log_b(n)

2) log_b(^m/_n) = log_b(m) – log_b(n)

3) log_b(mⁿ) = n · log_b(m)

$\log _a a = 1$ (since ) so $\log _7 7 = 1$
$\log _a 1 = 0$ (since ) so $\log _{20} 1 = 0$
$\log _a p + \log _a q = \log _a pq$ so $\log _3 2 + \log _3 5 = \log _3 10$
$\log _a p - \log _a q = \log _a {p \over q}$ so $\log _6 54 - \log _6 9 = \log _6 {{54} \over 9} = \log _6 6 = 1$
$\log _a p^n = n\;\log _a p$ so $\log _2 5^3 = 3\;\log _2 5$