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SingaporeAdditional MathematicsQuick questions
Logarithmic and Exponential Functions
Quick questions on Exponential and logarithmic equations: N(A)-Level Additional Mathematics
7short 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 exponential equations with matching bases?Show answer
If both sides can be written to the same base, equate the indices directly. For , write , so . This is the quickest route whenever it is available.
What are exponential equations needing logs?Show answer
When the bases cannot be matched, take logarithms of both sides and use the power law to bring the exponent to the front:
What are always check for invalid solutions?Show answer
You can only take the log of a positive number, so after solving a logarithmic equation, reject any solution that makes the inside of a log zero or negative. This final check is often worth a mark.
What is not combining logs before converting?Show answer
A sum of logs equal to a number must be combined into one log first; you cannot convert term by term.
What is q1?Show answer
Solve . [1 mark]
What is q2?Show answer
Solve , to 3 significant figures. [2 marks]
What is q3?Show answer
Solve . [2 marks]
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