SOLUTION: If {{{(3^r)=(4^s)=(24^t)}}}, find an expression for {{{t}}} in terms of {{{r}}} and {{{s}}}.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: If {{{(3^r)=(4^s)=(24^t)}}}, find an expression for {{{t}}} in terms of {{{r}}} and {{{s}}}.      Log On


   

Question 764905: If %283%5Er%29=%284%5Es%29=%2824%5Et%29, find an expression for t in terms of r and s.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
%283%5Er%29=%284%5Es%29=%2824%5Et%29
Find an expression for t in terms of r and s
24^t = 3^r
using natural logs
t*ln(24) = r*ln(3)
3.178t = 1.099r
t = %281.099r%29%2F3.178
t = .345687r
:
24^t = 4^s
using natural logs
t*ln(24) = s*ln(4)
3.178t = 1.386s
t = %281.386s%29%2F3.178
t = .4362s
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