Logarithmic Functions

• Domain: $x > 0$. Range: all reals.
• Passes through $(1, 0)$ and $(a, 1)$.
• Vertical asymptote: $x = 0$.
• Increasing function.

$y = \log_a(x - h) + k$: shift right $h$, up $k$. VA at $x = h$.

$y = \log_a x$ and $y = a^x$ are reflections in $y = x$.

$a^{\log_a x} = x$ and $\log_a(a^x) = x$.

$f(x) = \ln(x - 2) + 1$.

Domain: $x > 2$. VA: $x = 2$. Passes through $(3, 1)$.