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
Answer:
The error is in Step 1: the logarithmic equation was translated incorrectly. The base 4 should be raised to the exponent 3, so 2x − 12 = 4³ = 64. Then 2x = 76, and x = 38.