How do I solve 7.5=log(P/.0002) ?

Solve for P:
7.5 = log(5000. P)

7.5 = 15/2 and log(5000. P) = log(5000 P):
15/2 = log(5000 P)

15/2 = log(5000 P) is equivalent to log(5000 P) = 15/2:
log(5000 P) = 15/2

Cancel logarithms by taking exp of both sides:
5000 P = e^(15/2)

Divide both sides by 5000:
Answer: |  P = e^(15/2)/5000=0.36160848......THIS IS NATURAL LOG.

I am going to assume log base 10

 

7.5=log(P/.0002)

10^(7.5)=10^(log(P/.0002))

10^(7.5)=P/.0002

10^7*10^0.5*0.0002=P

 

10^7*10^0.5*0.0002 = 6324.555320336758664