CORE_MATH • SHS 1Term 1WAEC / WASSCE SyllabusVIP Lesson
Indices & Logarithms
Laws of indices, fractional and negative exponents, exponential equations, and fundamental properties of logarithms.
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Real-World Context & Relevance in Ghana
The Bank of Ghana and commercial banks use logarithmic formulas to determine the doubling time of mutual funds and Treasury bills under compound interest.
Key Syllabus Learning Objectives
- 1Apply the six core laws of indices to simplify complex algebraic fractions
- 2Solve exponential equations by equating bases or substitution
- 3Manipulate logarithmic expressions using product, quotient, and power rules
- 4Solve logarithmic equations and reject invalid extraneous roots
1
Solving Indicial Equations by Substitution
Equations of the form a^(2x) + b · aˣ + c = 0 can be converted into quadratic equations by substituting y = aˣ, ensuring y > 0.
- Recognize that 2^(2x) = (2ˣ)².
- Let y = 2ˣ, rewriting equation as y² + by + c = 0.
- Solve for y, then back-substitute to find x.
- Discard any negative values of y since aˣ cannot be negative for positive base a.
Core Takeaway:
Always remember to back-substitute to solve for the original variable x, not just y.
WAEC / WASSCE Examiner Tips
- When evaluating log expressions without tables, express numbers in terms of prime factors whose logs are given.
- Remember that the argument of a logarithm must be strictly positive (log(x) is undefined for x ≤ 0).
- Write out index laws explicitly to gain method marks.
Common Candidate Pitfalls & Errors to Avoid
- Assuming log(x + y) = log(x) + log(y) (which is completely invalid!).
- Forgetting that a^(1/2) means √a, not a / 2.
- Accepting negative roots for exponential terms like 3ˣ = -9.
Topic Mastery Checklist
- Can I convert 27^(2/3) to 9 without a calculator?
- Can I solve 2^(2x+1) - 9(2ˣ) + 4 = 0?
- Can I expand log(a²b/c³) using logarithmic laws?
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