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 \ - (1)/(3)`



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




`D: \\ \\ 4x+1 \ \textgreater \ 0 \\ \\ 4x \ \textgreater \ - 1 \\ \\ x \ \textgreater \ - (1)/(4)`



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