APFIVE Logarithm Quotient Rule
A researcher attempted to solve the equation $$\log(3*x)-\log(x-1)=1$$ by erroneously combining the logarithms as $$\log(3*x-(x-1))=1$$. What is the error in this approach and what is the correct method to combine the logarithms?
A
He subtracted the arguments instead of dividing them; the correct combination is $$\log\left(\frac{3*x}{x-1}\right)=1$$.
B
He should have added the logarithms together; the proper expression is $$\log(3*x+x-1)=1$$.
C
The error lies in misapplying exponent rules; the expression as given is already simplified.
D
No mistake was made; his approach is a valid operation on logarithms.
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