Exponentials & Logarithms

Exponential functions multiply by the same factor every step, and logarithms undo them. These articles explain growth and decay, what a logarithm actually asks, why the log laws mirror the exponent laws, and where the number e comes from.

Exponential Growth and Decay: Formula, Graphs and Examples
Exponential growth multiplies a quantity by the same factor every step, giving $f(x) = a \cdot b^x$ . When the factor $b$ is between $0$ and $1$ , the quantity shrinks instead: exponential decay.
What Is a Logarithm? Logs Explained Simply
A logarithm is an exponent. $\log_b x$ asks: what power of $b$ gives $x$? Since $2^3 = 8$ , $\log_2 8 = 3$ .
The Laws of Logarithms: Product, Quotient and Power Rules
The laws of logarithms turn multiplication into addition: $\log(MN) = \log M + \log N$ , $\log\frac{M}{N} = \log M - \log N$ and $\log(M^k) = k\log M$ . Each is an exponent law in disguise.
The Number e and the Natural Logarithm (ln) Explained
$e \approx 2.71828$ is the number that compound interest approaches when interest is added ever more often. The natural logarithm $\ln x$ is the logarithm with base $e$ .