Definition as inverse of exponential

What you'll learn

1. State that $\log_b x$ is the exponent to which $b$ must be raised to produce $x$, and convert between $b^y = x$ and $\log_b x = y$ in both directions
2. Evaluate $\log_b x$ without a calculator when the answer is an integer, a negative integer or a simple fraction, including $\log_b 1 = 0$ and $\log_b b = 1$
3. Bracket a non-integer logarithm between consecutive integers
4. Sketch $y = \log_b x$ as the reflection of $y = b^x$ in $y = x$, marking the $x$-intercept and vertical asymptote
5. Explain why $\log_b x$ requires $x > 0$