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Official 2023 Paper 2 · Q6

Paper 2Powers & logarithmsAlgebra

Consider the following equation where aa is a real number and a>1a>1:

(∗)ax=x.(*)\qquad a^x=x.

Which of the following equations must have the same number of real solutions as (∗)(*)?

  • I. log⁡ax=x\log_a x=x
  • II. a2x=x2a^{2x}=x^2
  • III. a2x=2xa^{2x}=2x
Anone of them
BI only
CII only
DIII only
EI and II only
FI and III only
GII and III only
HI, II and III

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