LogLab: $\log(x)$ & $\ln(x)$

Master Common & Natural Logarithms

Explore base $10$ ($\log_{10} x$) and base $e$ ($\ln x$), build exact evaluation speed, practice calculator approximations, and review step-by-step math breakdowns.

Base Basics & Mental Math

Practice exact mental math for $\log_{10}(x)$ and $\ln(x)$. Powers of $10$, powers of $e$, inverse properties ($\ln(e^x) = x$), and identity rules.

Exact Mental Answers

Calculator & Rounding

Practice decimal approximations using standard logarithmic properties and calculator rounding rules (to 2 or 3 decimal places).

Decimal Approximations

Mixed Master Challenge

A comprehensive mix of mental math evaluations, base identification, logarithm change-of-base rules, and decimal approximations.

Full Logarithm Review
Logarithm Key Rules & Cheat Sheet
Common Log Base $10$
$\log(x) = \log_{10}(x)$
Natural Log Base $e$
$\ln(x) = \log_{e}(x)$
Identities
$\log(1) = 0, \;\; \ln(e) = 1$
Inverse Powers
$10^{\log x} = x, \;\; \ln(e^x) = x$