Exponents, Roots, and Logarithms
Exponents repeat multiplication; roots undo them; logarithms ask which power produces a value. Each operation has domain rules worth stating before you calculate.
Powers and roots
b^n multiplies b n times. The nth root is the inverse—even roots of negatives are not real. Factorials and prime factorization live in the same arithmetic toolbox.
Logarithms
log_b(x) = ln(x)/ln(b). The argument must be positive; the base must be positive and not 1.