Find the constant k so that\(\log_{y^5}(x^3) = k \cdot\log_y(x)\) for all positive real numbers x and y with \(y \neq 1\)
Let z = logy5(x3) ---> (y5)z = x3 ---> y5z = x3
Then z = k·logy(x) ---> z/k = logy(x) ---> yz/k = x
Substituting: y5z = ( yz/k )3 ---> y5z = y3z/k
---> 5z = 3z/k
---> 5 = 3/k
---> k = 3/5
