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.
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.