$\ln(ax+b)-\ln(cx+1)+e^{3}+\ln(cx+1)=5+\ln(cx+1)$
Simplify$e^{3}+\ln(ax+b)=5+\ln(cx+1)$
Apply log rules$e^{e^{3}}(ax+b)=e^{5}(cx+1)$
Solve $ e^{e^{3}}(ax+b)=e^{5}(cx+1):{\quad}x=\frac{e^{5}-e^{e^{3}}b}{e^{e^{3}}a-e^{5}c}$$x=\frac{e^{5}-e^{e^{3}}b}{e^{e^{3}}a-e^{5}c}$