指数和的倒数 [英] reverse of exponential sum

问题描述

帮助!!!

我试图在Excel中找到一种从指数值之和算出基数的方法.但是，它并不那么简单，因为第一个乘数与其他乘数不同

I'm trying to find a way, in Excel, to work out the base number from the sum of exponential values. However, it's not as straight forward as that because the first multiplier is different to the others

例如，可能存在:

First number : 10
10 * 3 = 30
30 * 1.5 = 45
45 * 1.5 = 67.5
67.5 * 1.5 = 101.25
when you add these together you get 253.75

(它不一定总是相同的乘数或乘以相同的次数)

(It won't always be the same multipliers or the same number of times it's multiplied)

鉴于我知道乘数是多少(第一个乘数为3，其余乘数为1.5)，我正在尝试制定一个公式，该公式将从其他值的总和(253.75)得出第一个数字(10).

Given that I know what the multipliers are (3 for first and 1.5 for the rest) I'm trying to work out a formula that will derive the first number (10) from the sum of the other values (253.75).

我希望这是有道理的

在此方面，我将不胜感激！

I'd appreciate any help at all on this!

推荐答案

您的3(初始乘数)在错误的位置.试试这个:

Your 3 (initial multiplier) is in the wrong place. Try this:

= 253.75 *(1-1.5)/((1-1.5)+ 3 *(1-1.5 ^(5-1))

在最后的(5-1)中，第5个是从原来可以找到原始数字的总数开始倒退的总数.

In the final (5-1), the 5 is the total number of steps backward from the total that one would find the original number.

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