It's been a good few years since I've had to touch logs with my job, however today I found myself trying to calculate 570=a(1.5)^n for a theoretical pressure system.
Something in my head from high school tells me that I need to use logs to solve for a and n. Admittedly I could do it using a graph but I'd quite like to be able to do logs again as I know they are useful.
So onto the question. Just how do I utilise logs to solve 570=a(1.5)^n for a and n.
So far I have used my basic knowledge and taken logs of both sides (possibly not correctly) to get -
Then I rearranged to get -
This is where i'm stuck. I haven't got 'a' so I can't do anything more at this point, can I?
The basic formula I am using is T=ap^n. My values for T and p are 570 and 1.5 respectively.
I have been told to work it out using T=570 when p=1.5 AND T=510 when p=1. I am an idiot and pieces of paper have two sides...
However if I implement this into my equation as above, I am still confused.I now have -
n=(log510)/(loga) and n=(log570)/(log1.5a)
Am I missing something here?