Two quantities P P\,P and Q Q\,Q are related, and the graph of log10P\log_{10} Plog10P against log10Q\log_{10} Qlog10Q is a straight line with gradient 1.5 which meets the vertical axis at 0.8.
Show that P P\,P and Q Q\,Q can be connected by the equation P=aQbP = aQ^bP=aQb and find the values of a a\,a and bbb, giving a a\,a to 3 significant figures.
62 exam-style questions on AQA A Level Maths 1.9 F: Exponentials and logarithms, covering 1.9.1 Exponential functions and their graphs, 1.9.2 Gradient of e^kx (A-level only), 1.9.3 Logarithms as inverse functions, 1.9.4 Laws of logarithms, 1.9.5 Solving exponential equations, 1.9.6 Logarithmic graphs to estimate parameters (A-level only), and 1.9.7 Exponential growth and decay. Each one has a worked solution and a mark scheme showing where the marks go.