SOLUTION: {{{ 4^(t+1)=5^t }}} solve for t. give exact answer (no decimals, keep it in logs and whatnot). thank you

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: {{{ 4^(t+1)=5^t }}} solve for t. give exact answer (no decimals, keep it in logs and whatnot). thank you      Log On


   

Question 365673: ++4%5E%28t%2B1%29=5%5Et+
solve for t. give exact answer (no decimals, keep it in logs and whatnot).
thank you
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
4%5E%28t%2B1%29=5%5Et
(t+1)*log(4) = t*log(5)
t*log(4) + log(4) = t*log(5)
t*log(5) - t*log(4) = log(4)
t*log(5/4) = log(4)
t = log(4)/log(1.25)
---------------------
4%5E%28t%2B1%29=5%5Et
4%2A4%5Et=5%5Et
5%5Et%2F4%5Et+=+4
%281.25%29%5Et+=+4
Use base change
t = log(4)/log(1.25)