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.
104 exam-style questions on OCR A Level Maths 1.6 Exponentials and Logarithms, covering 1.6.1 Properties of the exponential function, 1.6.2 Gradient of e^(kx) (A-level only), 1.6.3 Definition of the logarithm, 1.6.4 The natural logarithm function, 1.6.5 ln x as inverse of e^x, 1.6.6 Laws of logarithms, 1.6.7 Equations involving exponentials, 1.6.8 Reduction to linear form, and 1.6.9 Modelling using exponential functions. Each one has a worked solution and a mark scheme showing where the marks go.