Elsa tries to solve the following equation, and determines there is no solution. Is she correct? Explain. log2x = log2(3x + 5) + 4

Answer:

Using the change-of-base formula, graph y = ln(x)/ln(2) and y = ln(3x + 5)/ln(2) + 4. The graphs do not intersect. Algebraically, the equation gives x = -80/47, which is outside the domain x > 0. Therefore, the equation has no solution, and Elsa is correct.