Mathematics Advanced – Sample Short Answer Quiz

Let ln⁡(2) = x and ln⁡(3) = y. Find an expression for ln⁡(12) in terms of x and y.

Solve the following equation for x: 2e^3x-e^2x=0.

A horizontal line is drawn to cut the graphs y = e^x and y = 1/2 e^x at the points C and D. Draw a graph to show this information and show that the distance CD is constant (that is, it does not depend on the position where the horizontal line is drawn).

Solve e^{(2 ln⁡(x))} = x + 6.