A-LevelMathematicsLogarithmic and exponential functions9709/31 · Oct/Nov 2020 · Q46 Marks
Solve the equation log₁₀(2x + 1) = 2log₁₀(x + 1) – 1. Give your answers correct to 3 decimal places.
- Solve the equation log₁₀(2x + 1) = 2log₁₀(x + 1) – 1. Give your answers correct to 3 decimal places.[6]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- State or imply log₁₀10 = 1
- Use law of the logarithm of a power, product or quotient
- Obtain a correct equation in any form, free of logs e.g. (2x + 1)/(x + 1)² = 10⁻¹ or 10(2x + 1)/(x + 1)² = 10⁰ or 1 or x² + 2x + 1 = 20x + 10
- Reduce to x² -18x-9=0, or equivalent
- Solve a 3-term quadratic
- Obtain final answers x = 18.487 and x = -0.487 Must be 3 d.p. Do not allow rejection.
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