To apply log transform on a variavble equation and transform to log variable the equation.

Look for a function where I can use it for a log transform on a equation and it will output the equation with log transformed variables.

For example: f=x^2*y^2

log transform on this will result in equation of 2a+2b where a and b are defined by x=e^a and y=e^b.

Similarly the inverse log transform can be used on equations.

If anyone of know any information please send me.

-Pavan

Answer 1

[Walter Roberson]

Symbolic toolbox.

However, your proposed transform is not correct.

Suppose x = -1 and y = e^3, then x^2*y^2 = 1*(e^3)^2 = e^6, and ln(e^6) is 6.

If x=e^a and x=-1 then -1=e^a, ln(-1)=a, a = I*Pi; If y=e^b and y=e^3 then e^3=e^b, b=3; 2*a+2*b = 2*Pi*I + 2*3 = 2*Pi*I + 6

We can see, though, that 6 is not 2*Pi*I + 6. The transform is thus at most valid over non-negative real values.

[Paulo Silva]

Walter I was looking into the question and I'm stuck with a problem

log(exp(2*a + 2*b)) , how can I force MuPad to simplify into just 2*a+2*b ?

[Walter Roberson]

Paulo, you would have to add assumptions about the range and data type of the values.

For example, in Maple if you had ln(f) = ln(x^2*y^2)

then,

simplify(%) assuming nonnegative

would give

ln(f) = 2*ln(x)+2*ln(y)

[Paulo Silva]

I just did this

a = sym('a','positive')

b = sym('b','positive')

and MuPad simplifies to 2*a+2*b :)

This goes into what Walter said about non-negative real values :)

[Paulo Silva]

thanks Walter, it's great to learn so much by trying to solve these problems :)

[PavanKumar S]

Here X is a non negative value and Paulo Silva's solution will work if function is simple product but what can be done in case where the function is a sum of product terms then how to apply the log transform and after some operation, need to apply the inverse transform too?

[Walter Roberson]

Maple is able to handle assumptions about expressions; I suspect MUPAD is as well.