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. 2023 Sep 11;13(9):754. doi: 10.3390/bs13090754
  • 4.

    Read the following material before answering the questions that follow:

 In general, the multiplication of n identical numbers a, denoted an, such as 23=8, when, 3 is called the logarithm with base 8 of 2, denoted log28 (i.e., 3=log28). In general, if an=b(a>0,a1,b>0) then n is called the logarithm of b with a as base, denoted logab (i.e., logab=n). If 34=81, 4 is called the logarithm of base 81 with 3, denoted log381=4.
(1) Calculate the value of each of the following logarithms:
log24 = _______; log216 = _______; log264 = _______.
(2) Observe what relationship is satisfied between the three numbers 4, 16, and 64 in (1)? What relationship is satisfied between log24,log216,log264?
(3) Based on (2), can you write a general conclusion?
logaM+logaN=______________(a>0, and a1, M>0, N>0)