O-LevelAdditional MathematicsLogarithmic and exponential functions4037/22 · Oct/Nov 2022 · Q24 Marks
Solve the equation 4e^(2x-3) = 7e^(5-x).
- Solve the equation 4e^(2x-3) = 7e^(5-x).[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [M1] e^(2x-3-(5-x)) = 7/4 oe or e^(5-x-(2x-3)) = 7/4 oe
- [M1] ln 4 + 2x - 3 = ln 7 + 5 - x oe, soi
- [A1] e^(3x-8) = 7/4 oe, soi or e^(8-3x) = 4/7 oe, soi
- [A1] ln 4 + 2x - 3 = ln 7 + 5 - x oe
- [M1] 3x - 8 = ln(7/4) oe or 8 - 3x = ln(4/7) oe
- [M1] 2x + x = ln 7 + 5 - ln 4 + 3
- [A1] x = (ln(7/4) + 8) / 3 oe or x = (ln 1.75 + 8) / 3 oe or 2.85[32...] rot to 3 or more sf
- [A1] x = (ln 7 - ln 4 + 8) / 3 oe or 2.85[32...] rot to 3 or more sf
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