Solve the exponential or logarithmic equation ln(x+1)-ln3=5

According to rules of logs, ln(x+1) - ln 3 = ln [(x+1)/3].

                                                           x+1
Then your equation becomes    ln [ ] = 8
                                                              3

Write the new exponential equation   e = e.

Raise the "e" on the left to the power ln [(x+1)/3].  Raise the "e" on the right to the power 8.  We get:

   x+1
= e^8
     3

Then x+1 = 3e^8, and x = 3e^8 - 1 (answer)