Question

Ln (−3x − 1) − ln 7 = 2 ln (4x + 1) − ln 3 = 5

Answer 1

$D: -3x - 1 \ \textgreater \ 0 \\ \\ -3x \ \textgreater \ 1 \\ \\ x \ \textless \ - \frac{1}{3}$


$\ln (-3x-1) - \ln 7 = 2 \\ \\ \ln ( \frac{-3x-1}{7}) = 2 \\ \\ \ln ( \frac{-3x-1}{7}) = \ln e^{2} \\ \\ \frac{-3x-1}{7} = e^{2} \\ \\ -3x - 1 = 7e^{2} \\ \\ 7e^{2} +1 = -3x \\ \\ \boxed{x = \frac{-7e^{2}-1}{3} }$



$D: \\ \\ 4x+1 \ \textgreater \ 0 \\ \\ 4x \ \textgreater \ - 1 \\ \\ x \ \textgreater \ - \frac{1}{4}$


$\ln(4x+1) - \ln 3 = 5 \\ \\ \ln ( \frac{4x+1}{3}) = 5 \\ \\ \ln ( \frac{4x+1}{3}) = \ln e^{5} \\ \\ \frac{4x+1}{3} = e^{5} \\ \\ 4x+1 = 3e^{5} \\ \\ 4x = 3e^{5} - 1 \\ \\ \boxed{x = \frac{3e^{5}-1}{4} }$