What volume of a 0.1 M H₃PO₄ will be required to neutralize 45.0 cm³ of a 0.2 M NaOH?

Logarithm answers: “what power gives this result?” If 10² = 100, then log₁₀(100) = 2. Logarithms are the inverse of exponentiation. Common log uses base 10; natural log (ln) uses base e ≈ 2.718.

Laws: log(xy) = log(x) + log(y), log(x/y) = log(x) – log(y), log(xⁿ) = n·log(x). These laws simplify complex calculations.

Applications: solving exponential equations, measuring earthquake magnitude (Richter scale), sound intensity (decibels), pH in chemistry. Logarithms compress large ranges into manageable numbers.