Natural log equations are solved by simplifying and rewriting the equation until the variable has been isolated on one side of the equation. At that point, a numerical value for the variable can be found and the equation is solved.
To begin solving the natural log equation, look for terms that include the natural log of one or the natural log of e (the base of the natural log, which is approximately equal to 2.718). The natural log of 1 is zero, and the natural log of e is one; these terms can be canceled out of the equation. Next, look for sums and differences of logarithms. The sum of two logarithms simplifies to the logarithm of the product of the two arguments. The difference of two logarithms simplifies to the logarithm of the quotient of the two arguments.
Logarithms with an exponent in the argument are simplified by turning the exponent into a constant multiplier. If there are logarithms with e to any power for an argument, those terms are equal to the number in the power because the natural logarithm of e is 1. Finally, rearrange the simplified logarithms until the variable is on one side of the equation and all remaining terms are one the other side.