A-LevelMathematicsLogarithmic and exponential functions9709/32 · Feb/Mar 2019 · Q15 Marks
Show that the equation log10(x - 4) = 2 – log10 x can be written as a quadratic equation in x.
- (i)Show that the equation log10(x - 4) = 2 – log10 x can be written as a quadratic equation in x.[3]
- (ii)Hence solve the equation log10(x - 4) = 2 – log10 x, giving your answer correct to 3 significant figures.[2]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.
- [M1] Use law for the logarithm of a product or quotient
- [M1] Use log10100 = 2 or 10² =100
- [A1] Obtain x²-4x-100 = 0, or equivalent
- [M1] Solve a 3-term quadratic equation
- [A1] Obtain answer 12.2 only
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