TMUA Official 2021 Paper 2 · Question 14

Official papers

Official 2021 Paper 2 · Q14

Paper 2Functions & graphsPowers & logarithmsAlgebra

Consider the following simultaneous equations, where $p$ is a real number:

\begin{aligned}p2^x+\log_2y&=2\\2^x+\log_2y&=1.\end{aligned}

What is the complete range of $p$ for which these simultaneous equations have a real solution $(x,y)$ ?

p<1

p\ne1

p>1

p<1

p>2

p\ne1

and

p<2

p>1

and

p<2

p>2

HAll real values of

p

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