Logarithms · Grades 12–12
Logarithm Worksheets
Read logₐ(n) as a question: a to what power gives n? Grade 12 worksheets for evaluating logs and solving exponential equations.
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What it is
A logarithm answers 'what power?', logₐ(n) = k means aᵏ = n. It's the inverse of an exponent.
Why it matters
Logarithms power exponential growth and decay, pH, decibels, and compound interest, and are essential for Grade 12 functions and calculus.
How to do it
- Read logₐ(n) as 'a to what power gives n?'.
- Rewrite as an exponent equation aᵏ = n if it helps.
- Find the exponent k.
Examples by level
- Beginnerlog₂ 2 =1
- Intermediatelog₂ 2 =1
- Advancedlog₈ 8 =1
Examples are generated by the same engine as the worksheets, so they're always mathematically correct. Built to avoid repeats, not reshuffle the same handful of questions.
Common mistakes
- Confusing the base with the argument.
- Forgetting logₐ(1) = 0.
- Mixing up which number is the exponent.
Tips
- logₐ(1) = 0 and logₐ(a) = 1 for any base a.
- A logarithm and an exponential with the same base undo each other.
For parents
Read logₐ(n) as a question: 'a to what power gives n?' Answering the question is the whole skill.
For teachers
Teach logs as the inverse of exponentials side by side so the relationship is explicit.
Key vocabulary
- logarithm
- the exponent a base must be raised to
- base
- the repeated factor
Frequently asked questions
- What is a logarithm?
- logₐ(n) is the exponent that base a must be raised to in order to get n, so log₂ 8 = 3 because 2³ = 8.
- How are logs and exponents related?
- They're inverses: aˣ = n is the same relationship as logₐ(n) = x.
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