Translate compact notation
Use powers, probability and a reduced sample space.
The idea
A logarithm states an exponent. Without replacement, the counts change between draws. Logical set statements can be chained when their conditions match.
A method to try
- Rewrite a logarithm as a power.
- Update the numerator and denominator after a draw.
- Trace membership through each stated rule.
Follow the reasoning.
Solve log₃(y) = 2, then check the solution.
- A logarithm specifies the exponent needed to obtain its argument from the base. The equation means 3² = y.
- Thus y = 9. Since the logarithm’s argument must be positive, the solution also satisfies the domain condition.
- Substitute it back: log₃(9) = 2. This check helps distinguish the argument, base and exponent rather than treating the logarithm as an unfamiliar symbol to manipulate mechanically.
Think it through first.
A bag starts with 5 tokens. After one token is drawn and kept out, what denominator is used for the probability of the second draw?
Show the explanation
4.
Without replacement, only four tokens remain; the favourable count may also change.
Make it your own
After reading, explain the method in your own words and identify the condition that makes it valid. Then try the linked starter practice without referring back to the worked example. Review the reasoning behind an error before repeating the same item; remembering an answer is different from being able to solve a new problem.
This lesson is one part of a short starter pathway. It does not cover the full exam syllabus or establish a predicted score.
Official references
These provider and publisher links explain the exam or underlying concepts. Our lessons and questions are original, independent practice.
View 18 references and checked dates
- CISIA: CEnT-S structure and syllabus (opens in a new tab)Checked 2026-09-20
- CISIA: CEnT rules (opens in a new tab)Checked 2026-09-20
- CISIA: practice simulations (opens in a new tab)Checked 2026-09-20
- Biology 2e: Laws of Inheritance (opens in a new tab)Checked 2026-09-20
Concept and scope reference. Our questions and explanations are original; no provider endorsement.
- Biology 2e: The Light-Dependent Reactions of Photosynthesis (opens in a new tab)Checked 2026-09-20
Concept and scope reference. Our questions and explanations are original; no provider endorsement.
- Chemistry 2e: Classifying Chemical Reactions (opens in a new tab)Checked 2026-09-20
Concept and scope reference. Our questions and explanations are original; no provider endorsement.
- Chemistry 2e: Atomic Structure and Symbolism (opens in a new tab)Checked 2026-09-20
Concept and scope reference. Our questions and explanations are original; no provider endorsement.
- College Physics 2e: Motion Equations for Constant Acceleration in One Dimension (opens in a new tab)Checked 2026-09-20
Concept and scope reference. Our questions and explanations are original; no provider endorsement.
- College Physics 2e: The Ideal Gas Law (opens in a new tab)Checked 2026-09-20
Concept and scope reference. Our questions and explanations are original; no provider endorsement.
- College Algebra 2e: Quadratic Functions (opens in a new tab)Checked 2026-09-20
Concept and scope reference. Our questions and explanations are original; no provider endorsement.
- College Algebra 2e: Inverse Functions (opens in a new tab)Checked 2026-09-20
Concept and scope reference. Our questions and explanations are original; no provider endorsement.
- College Algebra 2e: Systems of Linear Equations — Two Variables (opens in a new tab)Checked 2026-09-20
Concept and scope reference. Our questions and explanations are original; no provider endorsement.
- College Algebra 2e: Counting Principles (opens in a new tab)Checked 2026-09-20
Concept and scope reference. Our questions and explanations are original; no provider endorsement.
- Introductory Statistics 2e: Measures of the Center of the Data (opens in a new tab)Checked 2026-09-20
Concept and scope reference. Our questions and explanations are original; no provider endorsement.
- Introductory Statistics 2e: Frequency, Frequency Tables, and Levels of Measurement (opens in a new tab)Checked 2026-09-20
Concept and scope reference. Our questions and explanations are original; no provider endorsement.
- Prealgebra 2e: Solve Geometry Applications — Circles and Irregular Figures (opens in a new tab)Checked 2026-09-20
Concept and scope reference. Our questions and explanations are original; no provider endorsement.
- Contemporary Mathematics: Truth Tables for the Conditional and Biconditional (opens in a new tab)Checked 2026-09-20
Concept and scope reference. Our questions and explanations are original; no provider endorsement.
- ABO Blood Group — Medical Genetics Summaries (opens in a new tab)Checked 2026-09-20
Concept and scope reference. Our questions and explanations are original; no provider endorsement.