Solving log( X * Y+1))/Y = .98 where X is known (ie, finding Y)

[Enash]

Hi!

I need a bit of help with an equation I'm not really sure to go about breaking out. It is as follows.

log( X * Y+1))/Y = .98 Where X is a known quantity and we need to solve for Y.

I'm reaching an impasse where I can't break the log open. I know that e has a set approximate value but something about this seems impossible and my limited math skills are running into a brick wall.

Help if you can!

 

[mmm4444bot]

log( X * Y+1))/Y = .98 Where X is a known quantity and we need to solve for Y.

The left-hand side has mismatched grouping symbols.

Also, please use function notation, to make clear the logarithm's argument.

Have you tried applying any basic properties of logarithms? Please show what you've tried.

Be sure to read the forum guidelines, too. Thanks! :cool:

 

[Enash]

So quickly, I'm not a student, I'm a working professional in Visual Effects. I am just here for help, if you can't help me, that's fine. I am not taking a math course to figure this out.

Yes I applied the basic properties of logarithms as I could glean from wikipedia. It isn't as straight forward as you seem to think without someone there explaining it to you which is why I came here.

I honestly feel like your response is rude. It is super obvious that the extra ")" was a typo. If I have to endure treatment like this for a simple bit of help that is a HARD PASS for me.

There is a terrible culture here obviously. Guess I am used to programming websites and VFX websites where people are friendly and open to sharing/helping everyone.

The left-hand side has mismatched grouping symbols.

Also, please use function notation, to make clear the logarithm's argument.

Have you tried applying any basic properties of logarithms? Please show what you've tried.

Be sure to read the forum guidelines, too. Thanks! :cool:

 

[mmm4444bot]

I apologize for not recognizing that you're at work and the job requires X·Y+1 instead of X·(Y+1).

Using function name 'log' to denote the natural logarithm and X to represent a parameter:

log(X·Y+1)/Y = 0.98

If we multiply each side of this equation by Y, we get:

log(X·Y+1) = 0.98Y

This is a transcendental function of Y.

This is an algebraic function of Y.

There is no algebraic solution for Y, when these two types of functions are equated. A numerical algorithm is required to find Y once X is given, and an approximate value for Y (to whatever precision needed) is the result.

The only general solution for this type of equation (i.e., 'transcendental'='algebraic') that I've seen uses a convention known as the LambertW function.

Here's an implicit plot of Y, given some X values. The software that generated this plot used a numerical algorithm to determine Y for each (X,Y) point plotted.

For example, it determined that Y≈3.006679744 when X=6. This approximation for Y leads to 0.9800000003.