Power, Exponential & Logarithmic Functions

Logarithm Definition

$\log_{\color{#059669}a} {\color{#2563eb}y}$

$y$

$y > 0$

$a$ (base)

$a > 0, a \neq 1$

$\log_a x^n = n\log_a x$

$\log_a xy = \log_a x + \log_a y$

$\log_a \dfrac{x}{y} = \log_a x - \log_a y$

$\log_a b = \dfrac{\log_c b}{\log_c a}$

$\log_a b = \dfrac{1}{\log_b a}$

$\lg y = \log_{10} y$

$\ln y = \log_e y$

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

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

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