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,
$1.\,y>0$
$2.\,a>0,a\ne 1$
$1.\,y>0$
$2.\,a>0,a\ne 1$
Laws Of Logarithms
$1.\,\log_{a} x^n = n\log_{a} x $
$2.\,\log_{a} xy = \log_{a} x + \log_{a} y$
$3.\,\log_{a} \frac{x}{y} = \log_{a} x – \log_{a} y$
$4.\,\log_{a} b = \dfrac{\log_{c} b}{\log_{c} a}$
$5.\,\log_{a} b = \dfrac{1}{\log_{b} a}$
$2.\,\log_{a} xy = \log_{a} x + \log_{a} y$
$3.\,\log_{a} \frac{x}{y} = \log_{a} x – \log_{a} y$
$4.\,\log_{a} b = \dfrac{\log_{c} b}{\log_{c} a}$
$5.\,\log_{a} b = \dfrac{1}{\log_{b} a}$
Logarithms To Exponential
$x=\log_ay \Leftrightarrow y=a^x$
$\lg y=x \Leftrightarrow y=10^x$
$\ln y=x \Leftrightarrow y=e^x$
$\lg y=x \Leftrightarrow y=10^x$
$\ln y=x \Leftrightarrow y=e^x$
