Index laws and the laws of logarithms are essential tools for simplifying and manipulating exponential and logarithmic functions. There is an inverse relationship between exponential and logarithmic ...

\({\log _a}a = 1\) (since \({a^1} = a\)) so \({\log _7}7 = 1\) \({\log _a}1 = 0\) (since \({a^0} = 1\)) so \({\log _{20}}1 = 0\) \({\log _a}p + {\log _a}q = {\log _a ...

In Java, there is no built-in method to compute the logarithm of a number with a specific base directly. Instead, one typically uses: double log = Math.log(a) / Math.log(b), which can be verbose and ...

A method is given by which one may associate (uniquely) certain differential equations with analytic functions defined by certain Euler product expressions. Some of the consequences of this ...

Consider solving the Dirichlet problem $$\Delta u(P) = 0, P \in \mathbb R^2\backslash S,$$ $$u(P) = h(P),\quad P \in S,$$ $$\sup|u(P)| < \infty,$$ $$P \in \Bbb{R}^2 ...

Algebra is part of maths where we use letters to represent unknown values or values that can change. Simplify algebraic terms Algebraic expressions can be simplified by gathering like terms. Like ...