SOLUTION: Is there any way of simplifying z = [(ln x)/(ln y)]? I am using this as a growth factor and therefore e^z = e^[(ln x)/(ln y)] would also a be a good interpretation, however I

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Is there any way of simplifying z = [(ln x)/(ln y)]? I am using this as a growth factor and therefore e^z = e^[(ln x)/(ln y)] would also a be a good interpretation, however I      Log On


   



Question 736874: Is there any way of simplifying
z = [(ln x)/(ln y)]?
I am using this as a growth factor and therefore
e^z = e^[(ln x)/(ln y)]
would also a be a good interpretation, however I need to simplify the equation.

Found 3 solutions by lynnlo, ikleyn, mccravyedwin:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by ikleyn(53754) About Me  (Show Source):
You can put this solution on YOUR website!
.
Is there any way of simplifying
z = [(ln x)/(ln y)]?
I am using this as a growth factor and therefore
e^z = e^[(ln x)/(ln y)]
would also a be a good interpretation, however I need to simplify the equation.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


There is  highlight%28highlight%28NO%29%29  way to simplify expression   [(ln x)/(ln y)]   further.



Answer by mccravyedwin(421) About Me  (Show Source):
You can put this solution on YOUR website!

Yes, it can be simplified further because the ratio of two logs with the same 
positive base (not 1) is independent of the positive base (not 1). 


z%22%22=%22%22ln%28x%29%5E%22%22%2Fln%28y%29%5E%22%22%22%22=%22%22log%28k%2C%28x%29%29%2Flog%28k%2C%28y%29%29%22%22=%22%22log%28y%2C%28x%29%29%2Flog%28y%2C%28y%29%29%22%22=%22%22log%28y%2C%28x%29%29%5E%22%22%2F1%5E%22%22%5E%22%22%22%22=%22%22log%28y%2C%28x%29%29

Edwin