Solve the equation log _{3}(2 x-1)+log _{3}(x-1)=1 giving your answer in simplest form.

Question

Accepted Answer

Step:1 ：Combine the two logarithms using the product rule: (log _{3}((2 x-1)(x-1))=1)Step:2 ：Rewrite the equation in exponential form: ((2 x-1)(x-1)=3^1)Step:3 ：Expand the expression: (2x^2 - 3x + 1 = 3)Step:4 ：Solve for x: (2x^2 - 3x - 2 = 0)Step:5 ：Find the solutions: (x = -frac{1}{2}) and (x = 2)Step:6 ：Final Answer: (boxed{-frac{1}{2}}) and (boxed{2})

Answer

Step: 1 ：Combine the two logarithms using the product rule: (log _{3}((2 x-1)(x-1))=1)Step: 2 ：Rewrite the equation in exponential form: ((2 x-1)(x-1)=3^1)Step: 3 ：Expand the expression: (2x^2 - 3x + 1 = 3)Step: 4 ：Solve for x: (2x^2 - 3x - 2 = 0)Step: 5 ：Find the solutions: (x = -frac{1}{2}) and (x = 2)Step: 6 ：Final Answer: (boxed{-frac{1}{2}}) and (boxed{2})

Solve the equation $\log _{3}(2 x-1)+\log _{3}(x-1)=1$ giving your answer in simplest form.

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