This problem uses a form of the Arrhenius equation:
ln k2/k1 = -Ea/R(1/T2 - 1/T1)
k2 is the rate constant at temperature 2 (T2) = ?
k1 is the rate constant at temperature 1 (T1) = 295
Ea is the activation energy = 52.50 kJ/mol
k2/k1 = 7.50
R = 8.314 J/Kmol (note units of Ea; either change R or Ea to use same units)
Plug and chug and solve for T2