# The Quasi-Sequence

## If y = 10^x, then...

x | y |

0 | 1 |

log 2 | 2 |

log 3 | 3 |

log 4 | 4 |

log 5 | 5 |

log 6 | 6 |

log 7 | 7 |

log n | n |

## (log 1 = 0) But if n < *or* = 0, this trick won't work. In other words, it only works if n is positive.

## But wait, there's more!

x | y |

1 |
2 |

log23 | 3 |

2 | 4 |

log25 | 5 |

log2n | n |

y = 2^x

x | y |

1 | 5 |

log56 | 6 |

log57 | 7 |

log58 | 8 |

log5n | n |

y = 5^x

x | y |

0 | 1 |

1/3 | 2 |

log83 | 3 |

2/3 | 4 |

log8n | n |

y = 8^x

x | y |

0 | 1 |

logT2 | 2 |

logT3 | 3 |

logTn | n |

y = T^x (T ≠ 0 or 1; assume T is positive.)

## logaa = 1 (a ≠ 0 or 1; loga1 = 0; assume a is positive.)

## Amazing, isn't it?

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© Derek Cumberbatch