Standard +0.3 This question requires applying log laws (bringing down the coefficient, combining logs) and solving a resulting quadratic equation. While it involves multiple steps and log base 2 rather than natural logs, it follows a standard pattern taught in C2/C3 with no novel insight required. The algebraic manipulation is straightforward once the logs are eliminated, making it slightly above average difficulty but still routine.
Show that \(2 + \log_2(2x + 1) = 2\log_2(2^2 - x)\) leads to finding \(x\)
(6)
M1 Uses or states \(2\log_2(2^2 - x) = \log_2(2^2 - x)^2\); M1 Uses addition (or subtraction) law correctly; M1 Connects 2 with 4 OR \(2^2\) correctly and proceeds to form quadratic in \(x\); A1 Correct equation not involving logs in any form; M1 Solves quadratic by factorisation or completing square or correct formula use; A1 \(x = 12\) only and reject \(x = 40\)
Show that $2 + \log_2(2x + 1) = 2\log_2(2^2 - x)$ leads to finding $x$ | (6) | M1 Uses or states $2\log_2(2^2 - x) = \log_2(2^2 - x)^2$; M1 Uses addition (or subtraction) law correctly; M1 Connects 2 with 4 OR $2^2$ correctly and proceeds to form quadratic in $x$; A1 Correct equation not involving logs in any form; M1 Solves quadratic by factorisation or completing square or correct formula use; A1 $x = 12$ only and reject $x = 40$
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