A student solved log4(2x – 12) = 3, as shown.Step 1: 2x – 12 = 34Step 2: 2x – 12 = 81Step 4: 2x = 93Step 5: x = 46.5 Explain the error and find the correct solution.

Answer:

The student made an error in Step 1 by switching the base and the exponent when converting the logarithmic equation to exponential form. Instead of 3^4, it should be 4^3, because the base of the logarithm (4) becomes the base of the power. Correct Solution: 4^3 = 2x - 12 64 = 2x - 12 76 = 2x x = 38