Question

Solve. ln(–x + 1) – ln(3x + 5) = ln(–6x + 1) –0.67 or 2–1.58 or 0.14–0.14 or 1.58–2 or 0.67

Answer 1

From the given problem :

`\ln (-x+1)-\ln (3x+5)=\ln (-6x+1)`

Note that :

`\ln M-\ln N=\ln (M)/(N)`

The equation will be :

`\begin{gathered} \ln (-x+1)/(3x+5)=\ln (-6x+1) \\ (-x+1)/(3x+5)=-6x+1 \\ -x+1=(-6x+1)(3x+5) \\ -x+1=-18x^2-27x+5 \\ 18x^2+26x-4=0 \\ 9x^2+13x-2=0 \end{gathered}`

Using quadratic Formula :

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

a = 9, b = 13 and c = -2

`\begin{gathered} x=\frac{-13\pm\sqrt[]{13^2-4(9)(-2)}}{2(9)} \\ x=\frac{-13\pm\sqrt[]{241}}{18} \\ x=0.14 \\ \text{and} \\ x=-1.58 \end{gathered}`

The answer is :

x = 1.58 and 0.14