Changing from Decibel to normal with pdfs

Hi,

I have a distribution that is normal in the dB scale. When I convert it to the normal scale I cannot seem to get it to work for me.

For example I have a normal distribution with mean 0 variance 1.

I'm always adding 1 to numbers from that distribution and want to see the new pdf.

If I just generate variable x, then convert by

I can get the result but I want to be able to play with the pdfs.

Is there a way to do this correctly using only the pdfs?

I've tried converting the ranges but this leads to the problem of unevenly spaced bins.