Help rearranging complex formula

[sshinkwin]

Hi all,

I have an issue trying to rearrange this formula.

X = ( Z / (1 + 81 ^ ( ( A + B/2 - Y ) / B ) ) )

I am trying to rearrange this formula to make A the subject i.e. A = ......

Any help with this would be really appreciated.

Thanks

Stewart

 

[Deleted member 4993]

Hi all,

I have an issue trying to rearrange this formula.

X = ( Z / (1 + 81 ^ ( ( A + (B/2) - Y ) / B ) ) )

I am trying to rearrange this formula to make A the subject i.e. A = ......

Any help with this would be really appreciated.

Thanks

Stewart

Since you did not show any work - I assume you are stuck at the first step. The first step would be to isolate 'A' to the left-hand-side of the equation.

1 + 81^[(A + B/2)/B] = Z/X

Now continue.....

Please share your work with us ...

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

 

[sshinkwin]

Since you did not show any work - I assume you are stuck at the first step. The first step would be to isolate 'A' to the left-hand-side of the equation.

1 + 81^[(A + B/2)/B] = Z/X

Now continue.....

Please share your work with us ...

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

Thanks for your response. I can rearrange this formula to start with to get:


Z / X - 1 = 81 ^ ((A + (B/2) - Y) / B)

I also know that X = Y ^Z and that Y = X (1/Z). But i believe in this case you need to you LOG but i would struggle with this next step. Your help here would be appreciated.

Thanks

 

[Deleted member 4993]

Thanks for the reply. I can re-arrange to start with to get:

( Z / X ) - 1 = 81 ^ ( (A + (B/2) - Y) / B )

This is where i struggle. I know X = Y ^ Z can be rearrange to Y = X ^ ( 1 - Z). But i dont believe this helps in this situation. I believe you need to use LOG but i do not remember how to do this.

Your help here would be appreciated.

Thanks

That is incorrect.

However your step before that is correct.

( Z / X ) - 1 = 81 ^ [ (A + B/2 - Y) / B ]

Log{( Z / X ) - 1} = Log{9 ^ [ 2*(A + B/2 - Y) / B ]}

Log{( Z / X ) - 1} = [ 2*(A + B/2 - Y) / B ] * Log(9)

2*(A + B/2 - Y) / B = Log{( Z / X ) - 1} / Log(9)

Now continue....

 

[sshinkwin]

Thanks.

LOG [ ( Z - X ) / X ] / LOG ( 81 ) = [ A + ( B / 2 ) - Y ] / B

Rearranged to:

B * LOG [ ( Z - X ) / X ] / LOG ( 81 ) = A + ( B / 2 ) - Y

Rearranged to:

A = B * LOG [ ( Z - X ) / X ] / LOG ( 81 ) - ( B / 2 ) + Y

Is this right?

 

[sshinkwin]

Thanks, this works perfectly.

The original equation i had an inverse to that as well which was

X = ( - Z ) / ( 1 + 81 ^ P ) - Z , where P = [ A + ( B / 2 ) - Y ] / B

I subsequently rearrange to 81 ^ P = ( Z / - X + Z ) - 1

If A ^ X = B can be re-arranged to X = LOG (B) / LOG (A) then,

P = LOG [ ( Z / - X + Z ) - 1 ] / LOG [ 81 ]

However this is not working because ( Z / -X + Z) - 1 is a negative value.

Does anyone have any suggestions how to solve this. I am trying to make A the subject.

Thanks

 

[HallsofIvy]

The problem then is that your original formula, 81 ^ P = ( Z / - X ) + Z - 1, is not possible. 81 to a power cannot be negative.

 

[sshinkwin]

I had my origingal formula: X = ( Z / (1 + 81 ^ ( ( A + B / 2 - Y ) / B ) ) ) . I did not create this, this was taken from the internet.

Where:
A = Start of growth from 10% of saturation level
B = Time to get from 10% to 90% of saturation level
X = Adoption % in given year
Y = Given year
Z = Saturation level

With values of A = 2016.5 , B = 4 , Z = 100% it produce this adoption curve:



I was then able to rearrange this formula to show A as the subject: A = B * LOG [ ( Z - X ) / X ] / LOG ( 81 ) - ( B / 2 ) + Y

I then adjusted this original formula to show decay: X = ( - Z / (1 + 81 ^ ( ( A + B / 2 - Y ) / B ) ) ) – Z . With the same values as before this gave me a curve like:



I now want to re-arrange this decay formula to have A as the subject.

This is where I am struggling as I end up with the LOG of a negative value. Or have I rearranged incorrectly? Is there another way to show decay given my original equation?

 

[sshinkwin]

Yes apologies i have just got there myself.

Thanks for the help.