courses › Algebra

Growth by multiplying, and logs that answer “what power?”

Pen and paper is fine · no calculator needed why?

Learn first (about 3 minutes)

Opens at level 30.

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Builds on: Functions (not open yet) · Exponents & roots (not open yet)

skills · practice stats

From rounds of this course only: box, review and trial answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

• Solve for the exponent par 12 s not tried yet

  worked example

  Solve 2⁴ˣ = 16.

  Answer: 1

  1. 16 = 2⁴, so 4x = 4 and x = 1.

• Evaluate a log par 10 s not tried yet

  worked example

  What is log₂ 4?

  Answer: 2

  1. 2² = 4, so log₂ 4 = 2.

• Compound growth par 20 s not tried yet

  worked example

  $9,800 grows 20% per year, compounded yearly. What is it worth after 3 years?

  Answer: $16,934.40

  1. Multiply by 1.2 three times: $11,760, then $14,112, then $16,934.40.
  2. Check: $9,800 × 1.2³ = $16,934.40.

• Log rules par 15 s not tried yet

  worked example

  What is log₃ 45 − log₃ 5?

  Answer: 2

  1. Subtracting logs divides the insides: log₃ (45 ÷ 5) = log₃ 9.
  2. 3² = 9, so the answer is 2.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

1. 1 day
2. 3 days
3. 7 days
4. 14 days
5. 30 days
6. 60 days
7. mastered · every 90 days

your rounds

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