O-LevelAdditional MathematicsLogarithmic and exponential functions4037/21 · May/June 2023 · Q47 Marks
Solve the equation 5^(2y-1) = 6×3^y, giving your answer correct to 3 decimal places.
- (a)Solve the equation 5^(2y-1) = 6×3^y, giving your answer correct to 3 decimal places.[3]
- (b)Solve the equation e^(2x)-4+3e^(-2x) = 0, giving your answers in exact form.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- [M1] (2y-1) log 5 = log6 + ylog3 oe or 2y log 5 = log 30 + y log 3 oe
- [M1] Collects terms and factorises: y(2log 5-log 3) = log 6 + log 5 oe or y(2log 5-log 3) = log 30 oe
- [A1] 1.604 cao
- [M1] e^(4x)-4e^(2x)+3=0 or (e^(2x))^2 – 4e^(2x) +3=0 oe
- [M1] Factorises: (e^(2x) – 1)(e^(2x) – 3) oe or solves e^(4x) - 4e^(2x) + 3 = 0 oe
- [A1] e^(2x) = 1, e^(2x) = 3
- [A1] x = 0, x = (1/2)ln 3 or exact equivalent
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