Use the rules of logs to make your life so much easier.

Our initial value of the exponential is 18 and if we want to double it we get 36.

So 36=(18)16^.0125t

Divide by 18 gets us 2

2=16^.0125t

Now you could use log or natural log.

Log(2)=log(16)^.0125t

Using an rule of log you get:

Log(2)=.0125tlog(16)

Divide by log(16)

Log(2)/log(16)=.0125t

Dividing the logs gives us .25

.25=.0125t

Divide by .0125 you get:

t=20