1.To prove the Product Law of Logarithms: log_a​(MN)=log_a(​M)+log_a(​N), we let x=log_a(​M) and y=log_a(​N). Which of the following is the correct next step in the formal proof?
A.Write M=a^x and N=a^y, then consider the product MN.
B.Apply the power law log_a(​M^x)=xlog_a(​M) directly.
C.Write x=a^M and y=a^N, then multiply x and y.
D.Take the derivative of loga​x with respect to x.
2.Once we have MN=a^x⋅a^y=a^(x+y), which step completes the proof using the 'Hence' logic?
A.Conclude that log_a(​M)⋅log_a(​N)=log_a​(MN).
B.Substitute x=a^M into the equation.
C.Convert a^(x+y)=MN back to log_a​(MN)=x+y.
D.Divide both sides by a to get x+y=log(MN).
Solution
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