Thread: simplify logarithm

hi
i have the following
ln t = B1 + B2.T + B3.X + B4.X^2 + B5.X^3
where B1,B2,B3,B4,B5 are constants and X = ln y
i need this in a form t = C1 (y^C2) (e^(-C3/T))
where C1,C2,C3 are constants.
ln and e are natural log terms.
can this be done?
thanks
jas
p.s. i know e^(B3.X) = e^(B3. ln y) =e^(ln y^B3) = y^B3
but i'm not sure how to get the other terms B4.X^2 = B4 (ln y) (ln y)
and B5.X^3 = B5 (ln y) (ln y) (ln y)
in a similar form of y^??? (or if its possible!!)

Originally Posted by jas

hi
i have the following
ln t = B1 + B2.T + B3.X + B4.X^2 + B5.X^3
where B1,B2,B3,B4,B5 are constants and X = ln y
i need this in a form t = C1 (y^C2) (e^(-C3/T))
where C1,C2,C3 are constants.
ln and e are natural log terms.
can this be done?
thanks
jas
p.s. i know e^(B3.X) = e^(B3. ln y) =e^(ln y^B3) = y^B3
but i'm not sure how to get the other terms B4.X^2 = B4 (ln y) (ln y)
and B5.X^3 = B5 (ln y) (ln y) (ln y)
in a similar form of y^??? (or if its possible!!)

Taking the exponential of both sides,

Since x= ln y, so that is the same as .

So taking , , [tex], and you will have . I do not believe you can choose the constants so that it is rather than .

by
ln t = B1 + B2.T + B3.X + B4.X^2 + B5.X^3
i mean
ln t = B1 + B2.T + B3.(ln y) + B4.(ln y)(ln y) + B3.(ln y)(ln y)(ln y)
so (ln y)(ln y) is not the same as (ln y^2) = 2 ln y ?

so i don't know if the simplification you have is true?