2.1: Logarithm evaluations without a calculator

0606/21/M/J/16 — Question 3 · 6 marks · Log laws, Change of base, Equations

Do not use a calculator in this question.

(i)
Find the value of −log⁡pp2-\log_{p} p^{2}.
[1]
(ii)
Find lg⁡(110n)\lg\left(\dfrac{1}{10^{n}}\right).
[1]
(iii)
Show that lg⁡20−lg⁡4log⁡510=(lg⁡y)2\dfrac{\lg 20 - \lg 4}{\log_{5} 10} = (\lg y)^{2}, where yy is a constant to be found.
[2]
(iv)
Solve log⁡r2x+log⁡r3x=log⁡r600\log_{r} 2x + \log_{r} 3x = \log_{r} 600.
[2]