Provide an appropriate response.Prove that loga(M/N) = loga(M) - loga(N). Hint: Recognize that M = ax and N = ay.

Question

What will be an ideal response?

Answer 1

Answers will vary. One possibility is:

Using the properties of exponents:
 M/N =  = a^xa^-y = a^x-y.
By the definition of logarithm, M/N = a^x-y is equivalent to 
 log_a(M/N) = x - y.
Since M = a^x, then x = log_a(M), and since N = a^y, then y = log_a(N). Substituting, we get
 log_a(M/N) = log_a(M) - log_a(N).