Advanced Exponent Problems
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Lesson overview
Solving exponential equations by matching bases or taking logarithms.
Go to lesson quiz →Exam guidance · WAEC WASSCE Paper 1 + Paper 2 Lens
Pacing
Objective speed on Paper 1 + structured step-by-step method marks on Paper 2 Theory/Practical.
How WAEC marks this
Examiners award method marks (M1) for stating the formula/definition and accuracy marks (A1) ONLY when SI units are written.
Watch out for
Writing bare numbers without working or omitting SI units loses up to 50% of Paper 2 marks even when the final value is right.
Lesson content
Overview — Advanced Exponent Problems
Solving exponential equations by matching bases or taking logarithms. This lesson is at the advanced level — by the end, you'll be able to recognise this question type, apply a reliable method, and avoid the traps that cost marks.
Key Concept
An exponential equation has the unknown IN the exponent (e.g. 3^x = 81). It's solved either by expressing both sides with the SAME base and equating exponents, or (when that's not possible) by taking logarithms of both sides.
Why It's Tested This Way
Further Maths tests exponential-equation solving at Advanced level because it requires recognising WHICH method applies — same-base matching is faster when possible, but many real exponential equations require logarithms instead.
Method
To solve, first check whether both sides can be expressed as powers of the SAME base — if so, equate the exponents directly and solve the resulting simple equation; if not, take logarithms of both sides and use log rules to isolate the unknown.
Worked Example
Worked example: Solve 3^x = 81. Since 81 = 3^4, this becomes 3^x = 3^4, so by equating exponents, x = 4.
Second Worked Example
Second worked example: Solve 5^x = 20 (which can't easily be matched to a common base). Taking logs of both sides: x·log(5) = log(20), so x = log(20) ÷ log(5) ≈ 1.301 ÷ 0.699 ≈ 1.86.
Common Traps
Common trap: attempting to equate exponents when the bases are NOT actually expressible as the same base — always verify the bases genuinely match (or can be rewritten to match) before using the equate-exponents shortcut; otherwise logarithms are required.
Lesson Summary
Remember: (1) identify what is being asked, (2) apply the WAEC strategy, (3) check against the traps. Complete the 10-question quiz below to unlock the next lesson — you need at least 60% to pass.
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