SOLUTION: Use the functin below to solve for t in terms of the other variable. A= P (1+r/n)^nt

Algebra ->  Expressions-with-variables -> SOLUTION: Use the functin below to solve for t in terms of the other variable. A= P (1+r/n)^nt      Log On


   

Question 245456: Use the functin below to solve for t in terms of the other variable.
A= P (1+r/n)^nt
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
A=+P+%281%2Br%2Fn%29%5E%28nt%29
In general, to solve for a variable in an exponent we will use logarithms. But before that we should get rid of the P in front of the expression which is exponentiated. So we'll divide both sides by P:
A%2FP+=+%281%2Br%2Fn%29%5E%28nt%29
Now we find the log of each side. Any base can be used but choosing one that your calculator can do will make using the resulting equation easier to work with. So we will use base 10 logs:
log%28%28A%2FP%29%29+=+log%28%28%281%2Br%2Fn%29%5E%28nt%29%29%29
Now we can use a property of logarithms, log%28a%2C+%28p%5Eq%29%29+=+q%2Alog%28a%2C+%28p%29%29, to move the exponent of the argument out in front. This is how using logarithms allows us to get the variable out of an exponent!
log%28%28A%2FP%29%29+=+nt%2Alog%28%281%2Br%2Fn%29%29
And we can get t by itself by dividing both sides by n%2Alog%28%281%2Br%2Fn%29%29:
log%28%28A%2FP%29%29%2F%28n%2Alog%28%281%2Br%2Fn%29%29%29+=+t