A physics researcher is investigating the relationship between the intensity of light, yyy, and the distance, xxx, from a specialized laser source. The researcher finds that there is a linear relationship between log10y\log_{10} ylog10y and log10x\log_{10} xlog10x. The line representing this relationship passes through the points (1,7)(1, 7)(1,7) and (4,1)(4, 1)(4,1).
Determine an equation linking log10y\log_{10} ylog10y with log10x\log_{10} xlog10x.
Hence, or otherwise, express yyy in the form pxqpx^qpxq, where ppp and qqq are constants to be found.
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.