Question

Explain basic formula for Logs and Antilogs.

Answer 1

Logarithm Formula
Logarithms are the opposite phenomena of exponential like subtraction is the inverse of addition process, and division is the opposite phenomena of multiplication. Logs “undo” exponentials.
Trivial Identities
$lo{g}_b\left(1\right)=0;because{b}^0=1;b>0lo{g}_b\left(b\right)=1;because{b}^1=b$
Basic logarithm formulas
$lo{g}_b\left(xy\right)=lo{g}_b\left(x\right)+lo{g}_b\left(y\right)lo{g}_b\left(b\right)\left(\frac{x}{y}\right)=lo{g}_b\left(x\right)-lo{g}_b\left(y\right)lo{g}_b\left(x^d\right)=dlo{g}_b\left(x\right)lo{g}_b\left(\sqrt[y]{yx}\right)=\frac{lo{g}_b\left(x\right)}{y}clo{g}_b\left(x\right)+dlo{g}_b\left(y\right)=lo{g}_b\left(x^c{y}^d\right)$
Changing the base
$lo{g}_{b}a=\frac{lo{g}_d\left(a\right)}{lo{g}_d\left(b\right)}$
Addition & Subtraction
$lo{g}_b(a+c)=lo{g}_{b}a+lo{g}_b(1+\frac{c}{a})lo{g}_b(a-c)=lo{g}_{b}a+lo{g}_b(1-\frac{c}{a})$
Exponents
$x^{\frac{log\left(log\right(x\left)\right)}{log\left(x\right)}}=log\left(x\right)$