Keyword | CPC | PCC | Volume | Score |
---|---|---|---|---|

ln x 1 | 1.82 | 0.6 | 6467 | 56 |

ln x 1/2 | 1.37 | 0.1 | 9806 | 96 |

ln x 1/x | 0.47 | 0.7 | 9159 | 46 |

ln x 10 | 0.5 | 1 | 5509 | 71 |

ln x 1 dx | 0.57 | 0.6 | 3684 | 62 |

ln x 1 x 2 1/2 | 0.78 | 0.6 | 139 | 96 |

ln x 1 /log2x | 0.82 | 0.4 | 485 | 78 |

ln x 100 | 0.75 | 0.5 | 6300 | 89 |

ln x 1-x | 1.76 | 0.5 | 5688 | 9 |

ln x 1 x2 | 0.44 | 0.7 | 9102 | 29 |

ln x 1 泰勒展开 | 1.73 | 0.2 | 7903 | 21 |

ln x 1/x dx/1 x 2 | 1.06 | 0.4 | 7071 | 21 |

ln x 1 -ln x | 1.59 | 0.2 | 266 | 5 |

ln x 1 / x * dx / 1 x 2 | 0.36 | 0.7 | 6606 | 35 |

arctan x 1/2 ln 1 x/1-x | 1.24 | 0.4 | 3165 | 49 |

arctanh x 1/2 ln 1 x/1-x | 1.38 | 0.3 | 8228 | 86 |

g x x 1 ln 3 + t2 dt | 1.69 | 0.4 | 7866 | 2 |

g x x 1 ln 8 + t2 dt | 1.96 | 1 | 7679 | 54 |

y ln x 2-3x 1 | 1.84 | 1 | 832 | 66 |

y ln x 2-3x 1 3 0 | 1.11 | 0.4 | 5816 | 9 |

y ln x cos 14x | 1.19 | 0.5 | 9810 | 93 |

So this is 1 over delta x, and we're going to take the limit of everything. ln x divided by x is 1 plus delta x over x. Fair enough. Now I'm going to throw out another logarithm property, and hopefully you remember that-- and let me put the properties separate so you know it's not part of the proof-- that a log b is equal to log of b to the a.

ln ( x ⋅ y ) = ln x + ln y . {\displaystyle \ln (x\cdot y)=\ln x+\ln y~.} Logarithms can be defined for any positive base other than 1, not only e. However, logarithms in other bases differ only by a constant multiplier from the natural logarithm, and can be defined in terms of the latter.

The natural logarithm function ln (x) is the inverse function of the exponential function e x. The logarithm of the multiplication of x and y is the sum of logarithm of x and logarithm of y. The logarithm of the division of x and y is the difference of logarithm of x and logarithm of y.

The notations ln x and loge x both refer unambiguously to the natural logarithm of x, and log x without an explicit base may also refer to the natural logarithm. This usage is common in mathematics, along with some scientific contexts as well as in many programming languages.