Logarithm Quotient Rule

Question

To solve the equation $$\log(3x) - \log(x-1) = 1$$, a student incorrectly combined the logarithms, resulting in the equation $$\log(3x - (x-1)) = 1$$. Which of the following statements best describes the student's error and the correct method for combining the logarithms?

Accepted Answer

He subtracted the arguments instead of dividing them; the correct combination is $$\log\left(\frac{3*x}{x-1}\right)=1$$.

Answer

He should have added the logarithms together; the proper expression is $$\log(3*x+x-1)=1$$.

Answer

No mistake was made; his approach is a valid operation on logarithms.

Answer

The error lies in misapplying exponent rules; the expression as given is already simplified.

Logarithm Quotient Rule

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