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properties of logarithms

M

$M$ ,

N

$N$ ,

p

$p$ , and

b

$b$ are positive numbers and

b \neq 1

$b \neq 1$ , then the following properties apply:

{log}_{b} (1) = 0

$\log_{b} (1) = 0$

{log}_{b} (b) = 1

$\log_{b} (b) = 1$

{log}_{b} (b^{x}) = x

$\log_{b} (b^{x}) = x$

b_{b}^{{log}_{b} (x)} = x

$b^{\log_{b} (x)} = x$ , where

x > 0

$x > 0$

{log}_{b} (M \cdot N) = {log}_{b} (M) + {log}_{b} (N)

$\log_{b} (M \cdot N) = \log_{b} (M) + \log_{b} (N)$

{log}_{b} (\frac{M}{N}) = {log}_{b} (M) - {log}_{b} (N)

$\log_{b} (\frac{M}{N}) = \log_{b} (M) - \log_{b} (N)$

{log}_{b} (M^{p}) = p \cdot {log}_{b} (M)

$\log_{b} (M^{p}) = p \cdot \log_{b} (M)$

{log}_{b} (x) = {log}_{b} (y)

$\log_{b} (x) = \log_{b} (y)$ , then

{log}_{b} (x) = {log}_{b} (y)

$\log_{b} (x) = \log_{b} (y)$