Answer
1- To solve the logarithmic equation log4(2x – 12) = 3, you need to apply the correct logarithmic properties. 2- The student should have followed these steps: log4(2x-12) = 3 implies that 4^[log4(2x-12)] = 4^3. 3- According to the properties of logarithms, a^log_b(x) = x, thus we obtain 2x – 12 = 4^3, which simplifies to 2x – 12 = 64. 4- Now, we can solve for x: 2x = 76, leading to x = 38. The initial mistake lies in the assumption that 2x – 12 equals 34 instead of correctly equating it to 4^3.
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