Exponentials and logarithms

Find the value of log₃ 27 + log₃ 1/9. Circle your answer.

The temperature T °C of a cup of tea t minutes after it is made is modelled by T = 20 + 70e^-kt. After 10 minutes the temperature is 60°C. (a) Show that k = 1/10 ln 7/4. (b) Find the time taken for the tea to cool to 30°C. (c) Find the rate at which the tea is cooling when t = 10.

(a) Solve 3^2x - 10 × 3^x + 9 = 0. (b) Solve log₂(x + 3) + log₂(x - 3) = 4.