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 incorrectly swapping the base and the exponent when converting the equation from logarithmic form to exponential form. They used 3 as the base and 4 as the exponent ($3^4 = 81$) instead of using 4 as the base and 3 as the exponent ($4^3 = 64$). Correct solution: log4(2x – 12) = 3 2x – 12 = 4^3 2x – 12 = 64 2x = 76 x = 38