Cogito
Algebra 2 · Chapter 6 · Lesson 1
Logarithms as Inverses
The question "what power?" written down.
10 problems · about 21 minutes · F-BF.B.4, F-LE.A.4, A-SSE.B.3
What this lesson teaches
The student defines a logarithm as an inverse of an exponential and applies the laws of logarithms.
- A logarithm answers "what power?".
- It is the inverse of an exponential.
- Its laws are the exponent laws in disguise.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Graphing Radical Functions: y = √(x − 8). What is the smallest allowed value of x?
Answer 8
Why 8.
Review — Simplifying and Combining Radicals: √45 = a√5. What is a?
Answer 3
Why 3.
Warm Up
Straightforward practice. Get the method working first.
4 problemsWhat is log₄ 64?
Answer 3
Why 3.
Why does log(ab) = log a + log b?
Answer A logarithm is an exponent, and multiplying powers adds exponents.
Why Logs are exponents.
What is log₃ 27?
Answer 3
Why 3³.
What is log₅ 25?
Answer 2
Why 5².
Build It Up
The same ideas with more to keep track of.
2 problemsWhat is log₂ 1?
Answer 0
Why Anything to the power 0.
log 6 + log 5 = log of what number?
Answer 30
Why Adding logs multiplies.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Power: What is log₂ 32?
Answer 5
Why 5.
The Base Ten: What is log₁₀ 1000?
Answer 3
Why 3.