Given that $$\[ \ln (2 x+1)-\ln (x-3)=2, \]$$ find $$\(x\)$$ in terms of $$\(\mathrm{e}\)$$. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_w20_qp_23 Year：2020 Question No：1
Answer:
Use correct logarithm property to simplify left-hand side
Use correct process to obtain equation without logarithms
Obtain \(\frac{2 x+1}{x-3}=\mathrm{e}^{2}\)
Obtain \(x=\frac{3 \mathrm{e}^{2}+1}{\mathrm{e}^{2}-2}\)
Use correct process to obtain equation without logarithms
Obtain \(\frac{2 x+1}{x-3}=\mathrm{e}^{2}\)
Obtain \(x=\frac{3 \mathrm{e}^{2}+1}{\mathrm{e}^{2}-2}\)
Knowledge points:
2.2.1 understand the relationship between logarithms and indices, and use the laws of logarithms (excluding change of base)
Solution:
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