tmua.me Medium Set C Paper 2 · Question 16

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tmua.me Medium Set C Paper 2 · Q16

Paper 2Logic & proofPowers & logarithms

Let $x$ and $y$ be positive real numbers. Consider the conditions

\begin{aligned} P:&\quad x=y,\\[3pt] Q:&\quad \log_2(x+y)=1+\frac{\log_2x+\log_2y}{2}. \end{aligned}

Which statement correctly describes $P$ as a condition for $Q$ ?

ASufficient but not necessary

BNeither necessary nor sufficient

CNecessary but not sufficient

DBoth necessary and sufficient

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