Question

if y is equal to the logarithm of x to the base 5, what is the logarithm of x to the base 25 in terms of y?

Answer 1

First, set up a practical example for yourself to get a feel for what happens. Put X=5, and calculate log(X) to base 5 and you'll get 1.0. If on the other hand you calculate log(X) to base 25, you'll get 0.5. Now try changing X to something else, say 12. log(12) to base 5 is 1.544, whereas log(12) to base 25 is 0.772. There's a pattern emerging here: try a few more examples, and then try to formulate a general rule. (You can calculate logs to any base you like using the log function in MS Excel, if you have access to it.)

Answer 2

log₅ x = y , then 5^y = x

let log₂₅ x = z
then 25^z = x
(5^2)^z = x
5^(2z) = x or log₅ x = 2z

and z = (1/2)log₅ x

so log₂₅ x = (1/2)log₅ x

Answer 3

Thank you.
My math teacher and I were having a dispute over this problem; he thought it was y-2. I knew it was y/2, thank's so much!!