Natural Logarithms ```Name: juan a cornejo Status: N/A Age: N/A Location: N/A Country: N/A Date: N/A ``` Question: What is a natural logarithm? How would I solve one? High School Calculus Student. Replies: Let's talk about square roots first. If you have an equation X^2 = 4 then X = squareroot(4) = 2 If we have X^2 = 3.8 then X = squareroot(3.8) which we need a calculator or slide rule to find a numerical approximation to X (about 1.94936). Now, to logarithms. If you have an equation 2^X = 4 then X = logbase2(4) = 2 If we have an equation 10^X = 100 then X = logbase10(100) = 2 (because 10^2 = 100). There is a number called e which, like pi, pops up a lot in mathematics. The logbasee is called the "natural logarithm." So, sometimes you have an equation e^X = 100 to solve. From a calculator or slide rule, we can figure out that X = logbasee(100) = 4.60517... because e, which equals about 2.7182818... to the power 4.60517... equals 100! (try it on a calculator and see!) Sometimes the natural logarithm is indicated by ln and the base ten logarithm by log. so 10^x = 100; x = log(100) = 2; e^X = 100; X = ln(100) = 4.60517... best, prof topper Click here to return to the Mathematics Archives

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