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 (MEI) A Level Maths 1.8 Exponentials and Logarithms, covering 1.8.1 The function y = a^x, 1.8.2 Convert between index and logarithmic form, 1.8.3 Logarithm as inverse of exponential, 1.8.4 Laws of logarithms, 1.8.5 Values of log_a a and log_a 1, 1.8.6 Solve equations of the form a^x = b, 1.8.7 Reduce y = ax^n and y = ab^x to linear form, 1.8.8 The function y = e^x, 1.8.9 Gradient of e^kx (A-level only), 1.8.10 The function y = ln x, and 1.8.11 Exponential growth and decay. Each one has a worked solution and a mark scheme showing where the marks go.