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The magnitude (R) of an earthquake is related to its intensity (I) by , where T is the threshold below which the earthquake is not noticed.  If the intensity is doubled, its magnitude can be represented by

The speed of sound, v, at temperature T, in degrees Kelvin, is represented by the equation .  Which expression is equivalent to ?

A black hole is a region in space where objects seem to disappear.  A formula used in the study of black holes is the Schwarzschild formula, .  Based on the laws of logarithms, can be represented by

Banks use the formula when they compound interest annually.  If P represents the amount of money invested and r represents the rate of interest, which expression represents , where A represents the amount of money in the account after x years?

The equation used to determine the time it takes a swinging pendulum to return to its starting point is , where T represents time, in seconds, represents the length of the pendulum, in feet, and g equals .  How is this equation expressed in logarithmic form?