Question

Solve logarithmic equation
ln(3x + 1) - ln(5 +x) = ln 2

Answer 1

start with
\[\ln(\frac{3x+1}{x+5})=\ln(2)\] then go right to
\[\frac{3x+1}{x+5}=2\]

Answer 2

\[ \large
\begin{array}{rcl}
\ln(3x + 1) - \ln(5 +x) &=& \ln 2 \\
\ln\left(\frac{3x + 1}{5 +x}\right) &=& \ln 2 \\
e^{\ln\left(\frac{3x + 1}{5 +x}\right)} &=& e^{\ln 2} \\
\frac{3x + 1}{5 +x} &=& 2
\end{array}
\]

Answer 3

what @wio said, although since log is a one to one function you do not need to exponentiate
\[\ln(a)=\ln(b)\iff a = b\]