AP Precalculus / Unit 2: Exponential and Logarithmic Functions
2.11 Logarithmic Functions
Notes
$f(x)=a\log_bx$:
- Vertical asymptote $x=0$; passes through $(1,0)$.
- If $b>1$ and $a>0$: increasing and concave down.
- Grows very slowly: equal output increases need multiplicative input increases.
Practice
$\log_2x$ passes through:
$\log_21=0$.
The vertical asymptote of $\log(x-4)$:
Argument is 0 at $x=4$.
For $\log_{10}x$, going from 10 to 100 to 1000 raises the output by:
Multiplying input by 10 adds 1.
Ready for more? Take the Unit 2 test.