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4
The exponential is one-to-one.
A Level · English Medium · Pearson Edexcel · Mathematics
Number, fractions, decimals and percentages
Solve logarithmic and exponential equations with a valid domain.
About this lesson and its coverage
Original Kidemy A Level 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
Log laws concern positive arguments and suitable positive bases. Exponentials and logarithms are inverse functions. Algebra may produce candidates outside the domain, so check before accepting a root.
Worked example
ln(x−1)+ln(x+1)=ln8 gives x²−1=8. Candidate±3 leaves only x=3 because x>1.
- Identify the quantities and restrictions.
- Show a method with units or symbols.
- Check and explain the result.
Your written practice
Show your working on paper. Check your answer, then choose Next.
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4
3^4=81.
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3
x−2=1, with x>2.
Write in your own words. A guardian or teacher should review this response.
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x(x−3)=4 gives x=4 or −1; domain x>3 leaves4.
Show rejection of the invalid root.
Write in your own words. A guardian or teacher should review this response.
Show model answer and explanation
t=ln2/ln(1+r).
Cancel A, take logs and state the growth assumptions.
Progress and browser storage
Notebook challenge, sources and further study
Apply the idea
Create a logarithmic equation with an invalid algebraic candidate and explain the rejection.
Review with a guardian or teacher
- Use the stated evidence or givens.
- Show reasoning rather than only a result.
- Review and explain one correction.
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