# Solving Natural Logarithm Equations with ln and e

The problems in this lesson involve solving natural logarithm equations and leaving our answers in terms of ln and e. For example, to solve for x in the equation 'ln x = 3,' we convert the equation from logarithmic to exponential form, and we have e^3 = x, which is our answer in terms of e. Going in the other direction, if we're asked to solve for x in the equation e^x = 2, we convert the equation from exponential to logarithmic form, and we have 'ln 2 = x.' Finally, to solve ln x + ln (x + 5) = ln 36, we first condense the natural logs on the left side of the equation to get ln x(x + 5) = ln 36, then match up the numbers inside the natural logs to get x(x + 5) = 36, and solve from there. No ln calculator is required.