the rate constant of a reaction is 1.5*10^7 s^-1 at 100°C calculate the activation energy for the reaction?

With just the information you have provided, you cannot calculate the activation energy.

The relationship between the rate constant and the activation energy of a reaction is given by the Arrhenius equation. This equation can be written in several forms. The basic form is:

k = Ae^(-Ea/RT) where
k= rate constant
A = frequency factor
Ea = activation energy
R = gas constant
T = temperature in Kelvin

Without knowing the value of the frequency factor for this reaction, you cannot calculate the activation energy. Now, if there is additional information provided in the problem, you may be able to use this equation to solve for Ea. So, if you know the value of the frequency factor, then use the form of the equation given, or a modified form of that equation:

ln k = ln A - (Ea/RT)

Finally, if you are given the value of the rate constant at a different temperature, then you can use this form of the Arrhenius equation to calculate Ea:

ln (k2/k1) = -Ea/R (1/T2-1/T1) where
k1 is the rate constant at T1, and k2 is the rate constant at T2.