Power, Exponential, Logarithmic & Modulus Functions

🦉 Modulus Functions

For $|a| = b \Rightarrow a = b$ or $a = -b$.

🦉 Logarithm Definition

For $\log_a y$ to be defined,

1.\,y > 0

2.\,a > 0, a \neq 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 = \frac{\log_c b}{\log_c a}

5.\,\log_a b = \frac{1}{\log_b a}

🦉 Logarithms To Exponential

x = \log_a y \Leftrightarrow y = a^x

\lg y = x \Leftrightarrow y = 10^x

\ln y = x \Leftrightarrow y = e^x