A-LevelMathematicsLogarithmic and exponential functions9709/22 · May/June 2018 · Q47 Marks
Solve the equation 2ln(2x) – ln(x + 3) = 4 ln 2.
- (i)Solve the equation 2ln(2x) – ln(x + 3) = 4 ln 2.[5]
- (ii)Hence solve the equation 2ln(2^(u+1)) – ln(2^u + 3) = 4 ln 2, giving the value of u correct to 4 significant figures.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [B1] Use 2ln(2x) = ln(4x²)
- [M1] Use law for addition or subtraction of logarithms
- [A1] With no logarithms involved Obtain correct equation 4x²/(x+3) = 16 or equivalent
- [M1] Dependent on previous M1 Solve 3-term quadratic equation
- [A1] Conclude with x = 6 and, finally, no other solutions
- [M1] Apply logarithms and use power law for 2^u = k or 2^(u+1) = 2k where k > 0
- [A1] Obtain 2.585
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