Final answer:
The student's question is solved by applying properties of logarithms to simplify the equation, then solving the resulting quadratic equation for x.
Step-by-step explanation:
The question involves solving a logarithmic equation, which is a mathematical concept. To combine the logs on the right side of the equation, one can use the property of logarithms that states the logarithm of a product of two numbers is the sum of the logarithms of the individual numbers (log xy = log x + log y).
Furthermore, the equation given, 2 log(x) = log 2 + log(3x - 4), can be simplified using the property that states the logarithm of a number raised to an exponent is the product of the exponent and the log of the number (log(x^2) = 2 log(x)).
By applying these properties, the equation simplifies to log(x^2) = log(2(3x - 4)). Since the logarithms are equal, the arguments must be equal, leading to the equation x^2 = 2(3x - 4). Now, the student can solve for x by expanding and rearranging the equation into standard quadratic form and finding its roots using either factoring, completing the square, or the quadratic formula.