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 :

$\ln M-\ln N=\ln \frac{M}{N}$

The equation will be :

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

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