Theory question 103
Indices and Logarithms(a) Given that log10 p = a, log10 q = b and log10 s = c, express log10(p1/3q4/s2) in terms of a, b and c.
(b) The radius of a circle is 6 cm. If the area of the circle is increasing at the rate of 20 cm2s−1, find, leaving the answer in terms of π, the rate at which the radius is increasing.
Show the model answer
Model answer
(a) ⅓log p + 4 log q − 2 log s = a/3 + 4b − 2c.
(b) A = πr², dA/dt = 2πr dr/dt. 20 = 12π dr/dt, so dr/dt = 5/(3π) cm s⁻¹.
Explanation
Connect the rates with the chain rule.