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Learning Goal
Part of: Build new functions from existing functions — 3 of 3 cluster items
Understand inverse relationship of exponents and logarithms
HSF.BF.B.5
**HSF.BF.B.5**: (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
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HSF.BF.B.5: (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
What you'll learn
- State that the logarithm function y = log_b(x) is the inverse of the exponential function y = bˣ
- Convert between exponential form (bʸ = x) and logarithmic form (log_b(x) = y) fluently
- Evaluate logarithmic expressions by converting to "what exponent?" questions: log_2(8) = ? -> 2^? = 8 -> 3
- Use the inverse relationship to simplify compositions: b^(log_b(x)) = x and log_b(bˣ) = x
- Solve exponential equations using logarithms: bˣ = c -> x = log_b(c)
- Solve logarithmic equations using exponents: log_b(x) = c -> x = bᶜ
Prerequisites
Slides
Interactive presentations perfect for visual learners • 2 slide decks
Slide Video
Watch narrated slides play like a video lesson • Narrated slide playback
Task-sets
Learning resource • 1 task-sets