I typed about J Depp b/c K. Knightly was in Pirates of the Carribean...................she is also in the movie about Alan Turing.......




Logs, the number line...........and transcendental numbers.............what is Johnny D's ships log?  Capt. Sparrow.......................

Graph of the natural logarithm function. The function slowly grows to positive infinity as x increases and slowly goes to negative infinity as x approaches 0 ("slowly" as compared to any power law of x); the y-axis is an asymptote.

The natural logarithm of a number is its logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, log_e x, or sometimes, if the base e is implicit, logsimply x.^[1] Parentheses are sometimes added for clarity, giving ln(x), log_e(x) or log(x). This is done in particular when the argument to the logarithm is not a single symbol, to prevent ambiguity.

The natural logarithm of x is the power to which e would have to be raised to equal x. For example, ln(7.5) is 2.0149..., ebecause^2.0149... = 7.5. The natural log of e itself, ln(e), is 1, because e¹ = e, while the natural logarithm of 1, ln(1), is 0, since e⁰ = 1.