ThomasJones: There are probably some power series which can be used. A Web Search or a trip to a good library should provide the coefficients. The first post by BillyYank42 could be used, but might be a bit more time consuming than other methods. I am not sure what he meant by his second post: Reciprocal of exponential or inverse of exponential.

As suggested by BillyYank42, solve ex - Number = 0

When a value is found for the above, x = ln(Number) Id Est: Loge(Number) = x

You can find a value for x using the Newton method of successive approximations.

Note that ex is the derivative of F(x) = ex - Number, which is required when using the Newton method.