A-LevelMathematicsLogarithmic and exponential functions9709/33 · May/June 2023 · Q14 Marks
Solve the equation ln(x + 5) = 5 + lnx. Give your answer correct to 3 decimal places.
- Solve the equation ln(x + 5) = 5 + lnx. Give your answer correct to 3 decimal places.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- [M1*] Use exponentials or law for the logarithm of a product, quotient or power; Need e.g. ln((x+5)/x) = 5 or ln(x+5)= ln(e^5) + ln x or ln(x + 5) = ln(e^5 x) or x + 5 = e^5+lnx or x + 5 = e^5 e^lnx and others.
- [DM1] Correctly remove logarithms
- [A1] Obtain a correct equation in x e.g. (x+5)/x = e^5 (or 148.4...) or x + 5 = xe^5.
- [A1] Obtain 0.034; CAO Final answer must be 3d.p.
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