multiple regression with power law relationship [help!!!]

I am trying to carry out multiple regression of a dependent variable (DV)with 2 independent variables (IV1 & IV2) that exhibit power law relationship with the DV. i.e.

DV = a*IV1^b

and also

DV = c*IV2^d

where a,b,c,d are the coefficients of the power law relationships

When I plot them in scatter plot in excel.

Then, I want to look for a model that best describes the DV with both IV1 and IV2, and also understand the relative importance of IV1 and IV2. Therefore, I want to carry out a multiple regression.

I am using SPSS and linear regression is the easiest way to go.
If I have to take account of the power relationships, would the regression model predicator input in SPSS be: IV1^b and IV2^d ?
My concern is, it may be wrong to assume the same b and d still hold when the two IVs were put together in the regression.
But I am not very sure.

I also tried to log-transform both DV, IV1 and IV2 to run a linear regression, i.e.

ln(DV) = p*ln(IV1)+q*ln(IV2)+z
where p,q,z are regression coefficients.

The results are ok, but if I do the inverse log-transform, the relationship becomes,

DV = IV1^p*IV2^q*z

Which I am actually taking into account of the interaction of IV1 and IV2 instead of each superimposing on each other. And that doesn't sound right to me.

Another possibility is to use nonlinear regression in SPSS. But it's just a fitting and doesn't really tell you as much as running linear multiple regression (e.g. standardized coefficient, partial correlation, p-value of each IV for example)

Anyone has any insights on this? I tried to internet-search for a long time and couldn't find anything...:confused:

If you know anything please help me :wave: