tmua 2023 Q6

tmua · Uk · paper2 1 marks Laws of Logarithms Logarithmic Function Graph Intersection or Geometric Analysis

Consider the following equation where $a$ is a real number and $a > 1$ :
$$( * ) \quad a ^ { x } = x$$
Which of the following equations must have the same number of real solutions as $( * )$ ? I $\quad \log _ { a } x = x$ II $\quad a ^ { 2 x } = x ^ { 2 }$ III $a ^ { 2 x } = 2 x$
A none of them B I only C II only D III only E I and II only F I and III only G II and III only H I, II and III

..... 8

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

$$( * ) \quad a ^ { x } = x$$

Which of the following equations must have the same number of real solutions as $( * )$ ?
I $\quad \log _ { a } x = x$
II $\quad a ^ { 2 x } = x ^ { 2 }$
III $a ^ { 2 x } = 2 x$

A none of them
B I only
C II only
D III only
E I and II only
F I and III only
G II and III only
H I, II and III

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20