Exponential & Log Functions

Question

clearly explain, using correct mathematical terminology and graph transformations, the difference(s) between the graph of y = log₅𝑥 and y = log₅ (125^𝑥2). 

Answer 1

log5(125x^2) = log5(125) + log5(x^2) = 3 + 2 log5x

Thus, the second function stretches the first function by a factor of 2 and moves it up 3.