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6
2^6=64.
Class 11 · English Medium · Pearson Edexcel · Mathematics
Number, fractions, decimals and percentages
Solve exponential and logarithmic equations with domains stated.
About this lesson and its coverage
Original Kidemy Class 11 progression. This level has its own text, examples and questions. Curriculum versions share the progression; complete board-specific coverage still needs specification matching and additional material.
Learn the idea
For positive a≠1, log_a x is the exponent producing x and requires x>0. Logarithm laws apply to products and powers, not arbitrary sums. Exponential growth assumes a specified rate over specified intervals.
Worked example
log₂(32)=5. ln(x)+ln(2)=ln(10) gives 2x=10 and x=5, within x>0.
- Identify the quantities and restrictions.
- Show a method with units or symbols.
- Check and explain the result.
Your written practice
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4
3^4=81.
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1
e^0=1.
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The sum of logs equals ln(ab), not the log of a sum. For a=b=1, ln2 differs from 0.
Give a valid positive counterexample.
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Show model answer and explanation
x−1=100, so x=101, satisfying x>1.
State the logarithm argument restriction.
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Notebook challenge, sources and further study
Apply the idea
Create a logarithmic equation, solve it and reject any candidate outside its domain.
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- Use the stated evidence or givens.
- Show reasoning rather than only a result.
- Review and explain one correction.
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