Final answer:
The error in the solution is that the student did not correctly apply the exponentiation step when solving the logarithmic equation. The correct step is to express the equation as 'log x = log 27' and then solve to find 'x = 27'.
Step-by-step explanation:
The error in the student's solution lies in the step where the logarithm properties are applied. The student correctly uses the property of logarithms that states the logarithm of a number resulting from the division of two numbers is the difference between the logarithms of the two numbers (log x - log 3 = 2). However, when writing log x = 3log 3, the student makes an error by not applying the exponentiation correctly.
To correct the solution, you must apply the property that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. In this case, since log 3 = log 31, we exponentiate 3 by using the property in reverse to get log x = log 33 which then simplifies to log x = log 27, and by taking anti-logarithms of both sides, the final answer should be x = 27.
Remember that to solve equations involving logarithms, you may often need to apply other properties or operations of logarithms, such as exponentiation or converting back and forth between logarithms and exponents, to simplify and find the unknown.