Problem

Solve: log(2x-4)-log(x+2)=0

Answer

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Answer

Final Answer: \(\boxed{6}\)

Steps

Step 1 ：The given equation is in the form of \(\log(a) - \log(b) = 0\). According to the properties of logarithms, \(\log(a) - \log(b)\) can be rewritten as \(\log\left(\frac{a}{b}\right)\). So, the equation can be rewritten as \(\log\left(\frac{2x-4}{x+2}\right) = 0\).

Step 2 ：The equation \(\log(x) = 0\) is equivalent to \(x = 1\). Therefore, \(\frac{2x-4}{x+2} = 1\). Solving this equation will give us the value of x.

Step 3 ：Solving the equation gives us the solution x = 6. This is the value that makes the original equation true.

Step 4 ：Final Answer: \(\boxed{6}\)

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