Trying to write an equation for repeated division

[pintailpale]

I am struggling to remember my algebra and would appreciate some help.

I am trying to express how to calculate a series of dilutions. I am starting with a value of 150 and want to show that multiplying by a variable (z) 8 times should result in a value of 0.6. I might be way off, but the best I can come up with is (150*z)z)z)z)z)z)z)z)=0.6 but I don't know how to simplify and complete the equation from there. Hacking in excel leads me to believe z should be close to 0.502 but I'd like to get an equation I could use for other starting and ending values.

Thanks!

Value	0.502​
High	150​
1	75.3​
2	37.8006​
3	18.9759​
4	9.5259​
5	4.782​
6	2.40057​
7	1.20508​
Low	0.60495​	0.6​

 

[Deleted member 4993]

I am struggling to remember my algebra and would appreciate some help.

I am trying to express how to calculate a series of dilutions. I am starting with a value of 150 and want to show that multiplying by a variable (z) 8 times should result in a value of 0.6. I might be way off, but the best I can come up with is (150*z)z)z)z)z)z)z)z)=0.6 but I don't know how to simplify and complete the equation from there. Hacking in excel leads me to believe z should be close to 0.502 but I'd like to get an equation I could use for other starting and ending values.

Thanks!

Value	0.502​
High	150​
1	75.3​
2	37.8006​
3	18.9759​
4	9.5259​
5	4.782​
6	2.40057​
7	1.20508​
Low	0.60495​	0.6​

You almost had it:

(150*z)z)z)z)z)z)z)z)=0.6 \(\displaystyle \ \to \ \ \) 150 * z⁸ = 0.6

z⁸ = 0.6/150 = 0.004

z⁴ = √( 0.004) = 0.06324555

z² = √( 0.06324555) = 0.2514866796

z = √( 0.2514866796) = 0.5015

However, in Excel you can type in cell

=(0.6/150)^(1/8)

and BAM - the answer will be there.......

 

[pintailpale]

Thanks!