Finding the formula for a Sigma Notation Problem

[crashbandacoot420]

Hello, I'm not sure if this is calculus/the right place to post, but here goes.

I'm trying to find a formula to represent a function in a program i'm writing (that's unrelated really).
The situation is this:

We have some numbers, say
x = 80
y = 5
z = 0.95
How would I write the formula to represent how many times x=x*z until x == y?
Sorry for the 'programmer notation', but i'm not sure how else to phrase this - which is part of my issue!

As the title suggests, I think I would use a Sigma Notation to represent adding the times x is multiplied by z until x equals y. But that's as far as I've got.

Thanks!

 

[crashbandacoot420]

For clarification: because this is used for programming, I know I can easily obtain the answer by simply incrementing a number every time the multiplication happens. But I am specifically looking for the formula that represents this situation, if that makes sense.

 

[pka]

We have some numbers, say
x = 80
y = 5
z = 0.95
How would I write the formula to represent how many times x=x*z until x == y?

I don't think that you have written what you mean to ask.
\(x\cdot z=(80)(0.95)=76\) is that what you mean?
Now \(x\cdot z^{54}=5.0137730615182665\) Is that more like it?

 

[Steven G]

.80*.95^x = 5 does not have an integer solution, so you can't do what you want.

 

[Otis]

… How would I write the formula to represent how many times [x is multiplied by z] until x [equals] y? …

Hi cbac420. In your example, the number of multiplications is not a Whole number.

One expression for the number you're thinking about is ln(y/x)/ln(z).

Googling ln(5/80)/ln(0.95) yields an approximation rounded to 10 decimal places: 54.0536293359

The function name 'ln' stands for 'natural logarithm'.

?

 

[crashbandacoot420]

Hi cbac420. In your example, the number of multiplications is not a Whole number.

One expression for the number you're thinking about is ln(y/x)/ln(z).

Googling ln(5/80)/ln(0.95) yields an approximation rounded to 10 decimal places: 54.0536293359

The function name 'ln' stands for 'natural logarithm'.

?

Thank you, that is exactly what I was looking for. I appreciate you also interpreting my confusing question.