Power, Exponential, Logarithmic & Modulus Functions

Modulus Functions

For $|a|=b \Rightarrow a=b\text{ or }a=-b$ .

Logarithm Definition

For $\log_a y$ to be defined,
$1.\,y>0$
$2.\,a>0,a\ne 1$

Laws Of Logarithms

$1.\,\log_{a} x^n = n\log_{a} x$
$2.\,\log_{a} xy = \log_{a} x + \log_{a} y$
$3.\,\log_{a} \frac{x}{y} = \log_{a} x - \log_{a} y$
$4.\,\log_{a} b = \dfrac{\log_{c} b}{\log_{c} a}$
$5.\,\log_{a} b = \dfrac{1}{\log_{b} a}$

Logarithms To Exponential

$x=\log_ay \Leftrightarrow y=a^x$
$\lg y=x \Leftrightarrow y=10^x$
$\ln y=x \Leftrightarrow y=e^x$