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p = principal r= rate in decimal a =amount or final total t = time in years i = accumulated interest Simple interest: i=prt therefore t = i/pr Compound interest: a=(1+r)^t alright I'm going to throw in logs (logarithms) baby therefore log a = log ((1+r)^t)=t x log (1+r) therefore t = log a / log (1+r)
You can calculate that on any scientific calculator - like the calculator on Windows (if you change the options, to display as a scientific calculator). Log base 4 of 27 is the same as log 27 / log 4. You can use logarithms in any base to calculate that - just use the same base for both logarithms.
You divide log 8 / log 16. Calculate the logarithm in any base, but use the same base for both - for example, ln 8 / ln 16.
If 2y = 50 then y*log(2) = log(50) so that y = log(50)/log(2) = 5.6439 (approx). NB: The logarithms can be taken to any base >1.
To calculate Delta t, you would subtract Universal Time or UT from Terrestrial Time or TT. Delta t would be the difference.