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  • Natural logarithm
  • }}x\neq 0,} then ln⁡(x)=ln⁡(2x2)=ln⁡(1+x−1x+11−x−1x+1)=ln⁡(1+x−1x+1)−ln⁡(1−x−1x+1).{\displaystyle \ln(x)=\ln \left({\frac {2x}{2}}\right)=\ln \left({\frac

  • LN
  • Look up ln in Wiktionary, the free dictionary. LN, Ln or ln may refer to: Lawful Neutral, an alignment in Dungeons & Dragons The Sims 3: Late Night, the

  • Ln (Unix)
  • The ln command is a standard Unix command utility used to create a hard link or a symbolic link (symlink) to an existing file or directory. The use of

  • Stirling's approximation
  • approximation involves the logarithm of the factorial: ln⁡(n!)=nln⁡n−n+O(ln⁡n),{\displaystyle \ln(n!)=n\ln n-n+O(\ln n),} where the big O notation means that, for

  • Beta distribution
  • 1-X=E⁡[(ln⁡X−ln⁡GX)(ln⁡(1−X)−ln⁡G1−X)]=E⁡[(ln⁡X−E⁡[ln⁡X])(ln⁡(1−X)−E⁡[ln⁡(1−X)])]=E⁡[ln⁡Xln⁡(1−X)]−E⁡[ln⁡X]E⁡[ln⁡(1−X)]=cov⁡[ln⁡X,ln⁡(1−X)]covGX,(1−X)=ecov⁡[ln⁡X,ln⁡(1−X)]{\displaystyle

  • Exponential distribution
  • q¯α(X)=11−α∫α1qp(X)dp=1(1−α)∫α1−ln⁡(1−p)λdp=−1λ(1−α)∫1−α0−ln⁡(y)dy=−1λ(1−α)∫01−αln⁡(y)dy=−1λ(1−α)[(1−α)ln⁡(1−α)−(1−α)]=−ln⁡(1−α)+1λ{\displaystyle {\begin{aligned}{\bar

  • Log-normal distribution
  • E[X∣X<k]=eμ+σ22⋅Φ[ln⁡(k)−μ−σ2σ]Φ[ln⁡(k)−μσ]E[X∣X⩾k]=eμ+σ22⋅Φ[μ+σ2−ln⁡(k)σ]1−Φ[ln⁡(k)−μσ]E[X∣X∈[k1,k2]]=eμ+σ22⋅Φ[ln⁡(k2)−μ−σ2σ]−Φ[ln⁡(k1)−μ−σ2σ]Φ[ln⁡(k2)−μσ]−Φ[ln⁡(k1)−μσ]{\displaystyle

  • Logarithm
  • n! = 1 · 2 · ... · n, is given by ln⁡(n!)=ln⁡(1)+ln⁡(2)+⋯+ln⁡(n).{\displaystyle \ln(n!)=\ln(1)+\ln(2)+\cdots +\ln(n).} This can be used to obtain Stirling's

  • Gamma distribution
  • (X)&=\operatorname {E} [-\ln p(X)]\\[4pt]&=\operatorname {E} [-\alpha \ln \beta +\ln \Gamma (\alpha )-(\alpha -1)\ln X+\beta X]\\[4pt]&=\alpha -\ln \beta +\ln \Gamma (\alpha

  • Natural logarithm of 2
  • OEIS) is approximately ln⁡2≈0.693147180559945309417232121458.{\displaystyle \ln 2\approx 0.693\,147\,180\,559\,945\,309\,417\,232\,121\,458.} The logarithm

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Astrological/horoscope meaning of ln. ln means: With a Life Path 8, your numbers are (8, 17/8, 26/8, 35/8). The Life Path 8 suggests that you entered this life armed with a plan to manage, organize and govern. They are very ambitious and goal oriented. They want to use your goals, their organizational skills and efficient approach to carve a satisfying niche for themselves. If you are a positive 8 equipped with enormous potential to develop large programs and ideas, and also possess the toughness and independence, you follow to the end. In short, you are born to be a leader.They know how to manage themselves and their environment. Your ability to judge the character and potential of the people around you works to your advantage. Much of the success in life comes from, how hard you work.This way of life is most likely to produce workaholics. But your ability to recognize and attack tasks in your efforts makes you able to draw the right people. It is a quality of inspiration in your makeup that you can be a great leader. They are practical and stable in their pursuit of great goals, and you have the courage, when it comes to taking on great responsibilities and opportunities to strive forward.With the life path number 8 you are focused on learning the satisfactions that are in the material world. The Life Path 8 produces many powerful people, confident and materially successful. Most of your concerns relate to money and learning the power that it brings. With the proper handling of your financial resources, you have the potential of becoming extremely wealthy.This way of life is perhaps their most concern as they are desirous of status as the ultimate measure of success. You want to be recognized for your hard work and achievements. Reaching the honors and acceptance in the management of the club is very important. Given these, you are suitable for doing very well and competing in the business world or the political arena.In relationships you are frank, honest and firm. You can be very romantic, but are careful that you are not too busy and preoccupied to show it. Lavish gifts is not always an adequate replacement for your dedication and personal affection. You have to mitigate a great need for close personal relationships and to somehow soften your style. You need time for love and keep it as a major project in your life.The negative 8 is dictatorial and often suppresses the enthusiasm of colleagues and others around your efforts. Often the strength of their own personality excludes close feelings for other people with whom they come into contact. Gains and material rewards are often issues of the utmost importance, even at the expense of family, home and rest. Dedication to success can become an obsession. Emotional feelings are often suppressed by the negative 8, isolation and loneliness are paramount. All Life Path 8 people must avoid discounting the opinions of others.

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    L: Meaning of L in the acronym ln means: The letter has a flat bottom and a vertically extending part that projects into the sky. L is aspiring, reckoning, methodical, logical and convincing. Its flat bottom on the earth shows desire for earthly things hence L is materialistics and active. L is flexible, successful, public, insightful and considerate.

    N: Meaning of N in the acronym ln means: N has two stable ends on the ground and two upwards displaying confidence. It is willing to explore upwards as well as downwards indicating intellectual curiosity. It becomes sluggish if its spaces get filled with water thereby wasting talent from less agility. This makes it easily affected, but good fortunes always come to it.

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