Common and natural logarithms

What you'll learn

1. Interpret $\log x$ written without a base as $\log_{10} x$, and $\ln x$ as $\log_e x$
2. Evaluate common and natural logarithms on a calculator, and check each result by converting to exponential form
3. Describe $e \approx 2.718$ as a fixed irrational constant between 2 and 3 — not a variable, and not the E of scientific notation
4. Evaluate $\log 1000$, $\log 0.01$, $\ln e$, and $\ln e^3$ without a calculator, using the definition alone
5. Order $\log_2 x$, $\ln x$, and $\log x$ for the same argument, and explain why a larger base gives a smaller logarithm
6. Bracket a common logarithm between consecutive integers