Problem

Find all solutions to the equation

Solution

First, we use the laws of logarithms to combine terms until we are left with a single logarithm on each side.

Next, we will exponentiate both sides to cancel out the logarithms, then use the quadratic formula to solve for x.

or

However, we must be careful in dealing with logarithms, since their domain is only the positive real numbers. In particular, x = –2 is not a solution since –2 is not in the domain of ln(x). Therefore the only solution to this equation is x = 4.