First, how to calculate the natural logarithm ln
1, using a scientific calculator
Most scientific calculators or computer software provide the function of calculating ln function. Usually, you only need to input the value to be calculated on the calculator, and then press the ln key to get the ln value.
Step 2 use mathematical formulas
Ln function can be approximately calculated by a specific mathematical formula. The most commonly used formula is Taylor series expansion: ln (x) ≈ (x-1)-(x-1) 2/2+(x-1) 3/3-(x-1) 4/4+. This series expansion can gradually increase the number of series terms in a given x range to obtain a more accurate approximation.
3. Numerical method
In addition to series expansion, numerical methods (such as dichotomy, Newton tangent method, etc. ) can also be used to calculate the ln function. These methods will use numerical approximation to get the approximate solution of ln function.
Second, expand information.
1 and the related application of logarithm
Logarithm has many applications both inside and outside mathematics. Some of these events are related to the concept of scale invariance. For example, each chamber of the Nautilus shell is a rough copy of the next chamber, scaled by a constant factor. This leads to a logarithmic spiral. Ben Ford's leading digital distribution law can also be explained by scale invariance. Logarithms can also interfere with self-similarity.
For example, the logarithmic algorithm appears in the algorithm analysis, and the algorithm is decomposed into two similar smaller problems, and their solutions are patched, and the problem is solved. The size of self-similar geometric shapes, that is, shapes whose parts are similar to the whole image, is also based on logarithm. Logarithmic scale is useful for quantifying the relative change of value relative to its absolute difference.
In addition, because the logarithmic function log(x) grows very slowly for larger x, the logarithmic scale is used to compress large-scale scientific data. Logarithm also appears in many scientific formulas, such as tsiolkovsky rocket equation, Fenske equation or Nernst equation.