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SingaporeAdditional MathematicsQuick questions

Logarithmic and Exponential Functions

Quick questions on Exponential and logarithmic equations explained: O-Level A-Maths

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are logarithmic equations with logs on both sides?
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If both sides are single logarithms of the same base, such as log⁡aP=log⁡aQ\log_a P = \log_a Q, then the arguments are equal: P=QP = Q. Combine each side into one logarithm first if needed, then equate the arguments and solve, again checking that every argument stays positive.
What is not combining logs first?
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A logarithmic equation with two log terms should be merged into one before converting to index form.
What is q1?
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Solve 2x=502^{x} = 50, to three significant figures. [3 marks]
What is q2?
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Solve ex=7e^{x} = 7, to three significant figures. [2 marks]
What is q3?
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Solve log⁡2(x−1)=4\log_2 (x - 1) = 4. [2 marks]

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