Mean of lognormal with base 2

Hi,

I am trying to figure out what the mean of a lognormal distribution that is in base-2 rather than in base-e. Could someone help with the derivation or at least with the formula itself?

The reason I ask is that I need to generate values with a known mean for a multiplicative process. Therefore, I can't use a simple transform to figure out the mean.

I can generate values for natural logarithms using the mean value of

but this doesn't work for base-2 logs.

Thank you very much.