This question is designed to be answered without a calculator. An object travels along the x-axis so that its position after t seconds is given by x(t) = 2t^2 – 5t – 18 for all times t such that t ≥ 0.

Which inequality describes all times t for which the object is traveling toward the right?

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: