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,
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