Show that the equation 2log2x=log2(x+a)+32\log_2 x = \log_2(x + a) + 32log2x=log2(x+a)+3, can be expressed in the form x2−8x−8a=0x^2 - 8x - 8a = 0x2−8x−8a=0
Given the equation 2log2x=log2(x+a)+32\log_2 x = \log_2(x + a) + 32log2x=log2(x+a)+3 has only one real root, find the possible values of aaa.
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.