2.12

Logarithmic Function Manipulation

about 30 min · 6 short parts · stop after any part
Three rules let you break one log apart or squash many logs into one.
You'll need this to solve log equations next lesson, and it explains why some log graphs are just shifted.

The path

  1. 1
    Logs, fast refresh
    You can answer log⁡28\log_2 8 and log⁡1000\log 1000 in your head.
  2. 2
    The 3 log rules
    You can use the product, quotient and power rules on numbers.
  3. 3
    Expand: one log → many
    You can break log⁡x3yz\log\dfrac{x^3\sqrt y}{z} into separate logs.
  4. 4
    Condense: many logs → one
    You can squash 2log⁡x−3log⁡y2\log x - 3\log y into one log.
  5. 5
    Change of base (calculator)
    You can find log⁡6200\log_6 200 on a calculator.
  6. 6
    What the rules do to graphs
    You can describe log⁡3(18−9x)\log_3(18 - 9x) as shifts and flips, with domain.