Review question

# If we arrange $2^x, 2x$ and $x^2$ by size, what orders are possible? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5156

## Suggestion

Which of the following have no real solutions?

(i) $2x<2^x<x^2\quad$ (ii) $x^2<2x<2^x\quad$ (iii) $2^x<x^2<2x\quad$
(iv) $x^2<2^x<2x\quad$ (v) $2^x<2x<x^2\quad$ (vi) $2x<x^2<2^x$

A (i) and (iii),$\quad$ B (i) and (iv),$\quad$ C (ii) and (iv),$\quad$ D (ii) and (v),$\quad$ E (iii) and (v)

Could we sketch the graphs of $y=2x$, $y=2^x$ and $y = x^2$?

Are there some values of $x$ for which you know the order?