Exponents, Logarithms, and Roots index

Use this as the local map for powers, exponentials, logarithms, and roots.

Start here

• Exponents, Logarithms, and Roots - overview of the power triangle.
• Exponentiation - powers, exponentials, identities, and inverse relationships.
• Logarithm - inverse of exponential functions and logarithm laws.
• Root - inverse of power functions and fractional powers.
• Growth and decay - applied exponentials and logarithms.

How the pieces fit

Given $b^n=x$:

• exponentiation finds the power $x$;
• logarithms find the exponent $n={\log }_{b}x$;
• roots find the base $b=\sqrt[n]{x}$.

This folder links naturally into Differentiation rules for derivatives of powers, exponentials, logarithms, and roots, and into Integral for antiderivatives such as $\int x^{n}dx$ and $\int \frac{1}{x}dx=\ln |x|+C$.

Physics links

Exponential growth and decay appear in cooling, radioactive decay, damping envelopes, and cosmology. Logarithmic scales are useful when a quantity spans many orders of magnitude; see Cosmology distance methods for distance modulus and magnitude-style thinking.

Things to practise

• Rewrite radicals as powers before differentiating.
• Use logarithms to solve $A{e}^{kt}=B$ type equations.
• Check domains before applying inverse operations.

Route through the folder

Read the overview first, then Exponentiation, then split into Root and Logarithm. Finish with Growth and decay to see why exponentials are not just algebraic notation but a modelling primitive.