Logarithms and Exponents · CAPE Integrated Mathematics

4 past-paper questions on Logarithms and Exponents, part of Foundations of Mathematics, from every CAPE Integrated Mathematics paper on Quelpr.

1. 2(a)(i)3 marks· CAPE Integrated Mathematics · 2016 · Paper 2Given that f(x) = 2 ln x^2 - ln x, show that f(x) can be rewritten as f(x) = ln x^3.
2. 2(a)(ii)5 marks· CAPE Integrated Mathematics · 2016 · Paper 2Hence, solve the equation 2 ln x^2 = 2 + ln x, giving your answer correct to 2 decimal places.
3. 2(a)(i)6 marks· CAPE Integrated Mathematics · 2017 · Paper 2Show that the expansion 2\log 2 - \frac{1}{2}\log 9 + 4\log 3, when expressed as a single logarithm is \log 108.
4. 2(a)(ii)3 marks· CAPE Integrated Mathematics · 2017 · Paper 2Solve \log (x + 3) = 1.