875 prompts matching "Structured question: solve a logarithmic equation with two conditions"
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Common Mistakes: Using the factor theorem before dividing
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Worked Example: Factorising a cubic into a linear and a quadratic factor
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Common Mistakes: Factorising fully, and knowing when to stop
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Show All Working: Solving a cubic that must first be rearranged
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Worked Example: Sentences that are not propositions
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Show All Working: Translating an English sentence into logical symbols
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Common Mistakes: Translating a symbolic statement back into English
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Worked Example: Conjunction in a three-variable truth table
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Show All Working: Reading the final column of a truth table
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Common Mistakes: Writing the converse, inverse and contrapositive of one statement
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Practice: What logical equivalence means
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Show All Working: The distributive laws in logic
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Common Mistakes: Simplifying a compound statement using the laws
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Worked Example: What a contradiction is
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Practice: Showing that a statement is a tautology
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Explain Back: Showing that a statement is a contradiction
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Show All Working: The negation of a tautology
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Common Mistakes: Deciding between tautology, contradiction and contingency
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Worked Example: Premises and conclusion
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Practice: Modus tollens
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