Find the constant k so that logy5(x3)=k⋅logy(x) for all positive real numbers x and y with y≠1.
log y^5 (x^3) = k log y (x)
Using the change-of base theorem
log x^3 log x^k
______ = ________
log y^5 log y
3 log x k log x
______ = _______
5 log y log y
3 log x log y = 5k log x log y
3 = 5k
k = 3/5
