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A Level Pure Mathematics

Logarithms and Exponentials Questions and Answers

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Question 1 of 6inequalities / indices

Solve the inequality $|3^{-3x} - 54| < 27$ .

Questions on this topic

Paper 1inequalities / indices
Solve the inequality $|3^{-3x} - 54| < 27$ .
Paper 1indices / simultaneous equations
Solve the simultaneous equations $2^x + 3^y = 5$ and $2^{x+2} - 3^{y+1} = 13$ .
Paper 1indices / exponential equations
Solve the equation $5^{x-1} + 5^{x-2} = 30$ .
Paper 1Exponentials and logarithms
Solve the equation $e^{2x} = 4e^{2-x}$ , giving your answer in exact form.
Paper 1Exponential equations
Solve the equation $3^{x-1} + 3^{x-2} = 12$ .
Paper 2Indices and logarithms
Simplify $\dfrac{3^{2x-3}\cdot81^{x+\frac12}}{27^x}$ , giving the answer as a single power of 3.

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Functions and Graphs Trigonometry Sequences and Series Complex Numbers Integration

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